# Form a polynomial f(x)

16,358 results

Math-Funtions
1)Expand and simplify. Express each equation in standard form. a) f(x) = -2(x-1)(x+4)(x+1)(x-3) b) f(x) = (x+2)(x+1)(x+4) c) f(x) = x(x-6) 2) For each function in question 1. state the degree of the polynomial and identify the type of function

Math-Functions
1)Expand and simplify. Express each equation in standard form. a) f(x) = -2(x-1)(x+4)(x+1)(x-3) b) f(x) = (x+2)(x+1)(x+4) c) f(x) = x(x-6) 2) For each function in question 1. state the degree of the polynomial and identify the type of function

Math---helpppp
1)Expand and simplify. Express each equation in standard form. a) f(x) = -2(x-1)(x+4)(x+1)(x-3) b) f(x) = (x+2)(x+1)(x+4) c) f(x) = x(x-6) 2) For each function in question 1. state the degree of the polynomial and identify the type of function

Algebra
Consider the following polynomial function F(x)=-2x^3-x^2+13x-6 to answer the following question. If (x+3) is a factor of f(x) rewrite f(x) in completely factored form and identify the zeros f(x).

algebra
solve the polynomial y=2x^2-4x+1 I am sure neither your text nor your teacher asked you to "solve the polynomial y=2x^2-4x+1 " are you graphing the function, or are you solving the quadratic y=2x^2-4x+1 ?

algebra
Volume of a Box (Refer to the preceding exercise.) A box is constructed from a square piece of metal that is 20 inches on a side. (a) If the square corners of length x are cut out, write a polynomial that gives the volume of the box. (b) Evaluate the polynomial when inches. (c...

Algebra 2
The Question(s):: Write the polynomial 2-2x+5x^2-2x^5 in standard form. a.) What is its degree? b.)What is the leading coefficient? I missed this lesson in class. It's very confusing. Could someone please explain what to do? Much appreciated, Rae

Algebra
Solve the polynomial x^2+35x+27 Is this polynomial equal to something? Assuming it is equal to zero x= (-35 +- sqrt (35^2 -4*27) )/2

Math - polynomial function
Write a polynomial function with integral coefficients having the given roots. 1.) 0, -1/2, 6 2.) +or- 5i

Algebra
What polynomial could you subtract from 5x^3 - 12x - x^2 + 9 - 12x^5 - 6x^4 to give a difference of 19 + 8x^3 - 18x - 19x^5 - 2x^2 - 8x^4? Is the answer k (the polynomial) = 7x^5 + 2x^4 - 3x^3 + x^2 + 6x - 28?

math
Find a cubic polynomial p(x) so that the solution of p(x) ≤ 0 is [-2,1] or [4,∞). Is your polynomial the only one that gives this solution? Explain.

Help Polynomial
A polynomial P(x) has remainder R x +S on division by (x-a) (x-b). If a is not equal to b, express the constants R and S in terms of a, b, P(a), P(b). Find the remainder when P(x) is divided by (x-a)^2.

Finding polynomial from zeros
How to find the polynomial degree 2 and zeros are (1+i) & (1-i) I would like to see the steps to solve this. Thanks. If those are the roots, then the following are factors: (x-1-i)(x-1+i)

Polynomial Function
Could you help me with the following problem, I don't understand how to do it. Find an nth degree polynomial function with real coefficients satisfying the given conditions. 1. n=3; 3 and i are zeros; f(2)=20

math
If the digits of a number may be any one of 0 through 9 (except the first digit cannot be zero), and the system of alternating signs of coefficients is used to create a polynomial, what is the least number m of real zeros the polynomial can have? What is the greatest number M ...

math
If the digits of a number may be any one of 0 through 9 (except the first digit cannot be zero), and the system of alternating signs of coefficients is used to create a polynomial, what is the least number m of real zeros the polynomial can have? What is the greatest number M ...

math
If the digits of a number may be any one of 0 through 9 (except the first digit cannot be zero), and the system of alternating signs of coefficients is used to create a polynomial, what is the least number m of real zeros the polynomial can have? What is the greatest number M ...

algebra question
Give an example of a polynomial with degree 3 such that when factored, it contains the two factors (x+5) and (2x-1), i.e., the polynomial looks like (x+5) (2x -1) ( ? ). How many such polynomials you think there are?

Math
Use the given information about a polynomial whose coefficients are real numbers to find the remaining zeros of the polynomial. Degree: 6 Zeros: -6 + 13i^3, -8 + s^2i, -3 - 4i

Polynomial
Arrange the terms of the polynomial in descending powers of p. 13rp-4r^4p^4-4r^2p^3 Is my answer correct? -4r^4p^4-4r^2p^3-13rp

Math - Trigonometry
Let f(x) be a polynomial such that f(cos theta) = cos(4 theta) for all \theta. Find f(x). (This is essentially the same as finding cos(4 theta) in terms of cos theta; we structure the problem this way so that you can answer as a polynomial. Be sure to write your polynomial ...

algebra
explain in your own words how to factor a polynomial of the the form ax^2 + bx+c when A is not equal to 1. Describe both the grouping approch as well as reversing FOIL. Contrast the two methods by means of an example. Which is the best approach and why>

Algebra
2pi(x^2 + 4x + 4) + 2pi(x^2 + 7x + 10) How do I write this as a polynomial in standard form (by factoring out 2pi)?

Algebra
Write a polynomial of least degree with real coefficients and with the root -6-8i. Write your answer using the variable x and in standard form with a leading coefficient of 1. Thanks, I have no idea!

Precalculus
Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed. 2(multiplicity 2), -4(multiplicity 3)

Precalculus
Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed. 3(multiplicity 2), 5+i(multiplicity 1)

Math (Algebra)
A number is called algebraic if there is a polynomial with rational coefficients for which the number is a root. For example,√2 is algebraic because it is a root of the polynomial x^2−2. The number √2+√3+√5 is also algebraic because it is a root ...

college algebra
1. find the equation of the line with the given properties. Express the equation in general form or slope-intercept form. perpendicular to the line -3x_y= -27; contains the point (9, -1) the equation of the line is ? 2. solve the polynomial inequality and then graph the ...

Algebra 2
Given that the polynomial has the given root, find all roots of the polynomial. P(x) = x^4 - 5x^3 + 7x^2 - 5x + 6; -i

Polynomial
Create a polynomial that describes the perimeter of the outside figure: x + 8, 5, x, x, 2x, x + 8, 34 and inside figure: x + 12.

Math
Let f(x) be a polynomial such that f(cos theta) = cos(4 theta) for all theta. Find f(x). (This is essentially the same as finding cos(4 theta) in terms of cos theta; we structure the problem this way so that you can answer as a polynomial. Be sure to write your polynomial with...

algebra plus
The base of a rectangular box is x +2 cm wide and 2x+5 cm long. if the height of the box is x cm, write a polynomial in standard form which represents the box's volume

Math
Find the discriminant for the quadratic equation f(x) = 5x^2 - 2x + 7 and describe the nature of the roots. discriminant is 144, one real root discriminant is -136, two complex roots <--? discriminant is -136, one complex root discriminant is 144, two real roots If a ...

math
For every positive integer n, consider all monic polynomials f(x) with integer coefficients, such that for some real number a x(f(x+a)−f(x))=nf(x) Find the largest possible number of such polynomials f(x) for a fixed n<1000. Details and assumptions A polynomial is ...

math
The graph of a second-order polynomial is shown below, and the intercepts with the axes are marked. Explain how you can use the graph to write the polynomial as a product of linear factors (x-a)(x-b). Be sure to state the values of a and b.

Math
Given a polynomial and one of its factors, find the remaining factors of the polynomial. Some of the factors may not be binomials. 169x^3-1690x^2-9x+90; x-10

Math - Fundamental Theorem
We can actually use the Zeros Theorem and the Conjugate Zeros Theorem together to conclude that an odd-degree polynomial with real coefficients must have atleast one real root (since the non-real roots must come in conjugate pairs). But how can we get the same conclusion by ...

Calculus
Form a polynomial, f(x) with real coefficients having the given degree and zeros. Degree: 4 ; Zeros: 4i and 5i Really need help! don't know where to start.

calculus
form a polynomial with real coefficients have given degree and zeros. degree 5, zeros 9, -i; 8+i please show work

Algebra ll
Please help!! I do not understand any of this!! Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros: 2, multiplicity 2; 3i

college algebra
Form a polynomial, f(x), with real coefficients having the given degree and zeros. Degree 3; zeros: 1 + i and -10

College algebra
Form a polynomial f(x) with real coefficents having the given degree and zeros degree 5; zeros: 5; -i; -9 +i f(x)=a

College algebra
Form a polynomial f(x) with the real coefficients having the given degree and zeros. Degree 5; Zeros: -3; -i; -6+i f(x)=a( )

College Algebra
Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 5; Zeros: -3; -i; -6+i F(x)=a ( )

College Algebra! help!
Form a polynomial f(x) with the real coefficients having the given degree and zeros. Degree 5; Zeros: -4; -i; -2+i f(x)=a( )

elgebra
indentify the degree of each term of yje polynomial and the degree of the polynomial -2X^3+3x^2+4x+9

Connexus
Suppose you divide a polynomial by a binomial. How do you know if the binomial is a factor of the polynomial?

algebra
What is the complete factored form of the following polynomial? 40u^2v + 50uv^2 a) 10u(4uv + 10v^2) b) 5u(8uv + 10v^2) c) 10uv(4u + 5v) d) 5v(8u^2 +10uv) Thanks!!!!!!!!!!!!!!!

math
how do i represent 1/(1+x^4) in general taylor polynomial. I know the pattern is 1-x^4+x^8-x^16..... I don't know how to represent this pattern in variables equation form

math
how do i represent 1/(1+x^4) in general taylor polynomial. I know the pattern is 1-x^4+x^8-x^16..... I don't know how to represent this pattern in variables equation form

Algebra
Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 5; zeros:1;-i; -7+1

Algebra
Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree: 4; zeros: -1, 2, and 1-2i

Algebra
Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree: 4; zeros: -1, 2, and 1-2i

Algebra II
Factor the Polynomial in quadratic form. 6y(to the sixth power) - 5y(to the third power) - 4 6y^6 - 5y^3 -4 = (2y^3 + 1)(3y^3- 4) I do not believe the cubic terms are separable into quadratic factors.

Algerbra
A rectangular flower garden is 4 feet longer than its width w. Write a polynomial that represents the area of the garden. Write your answer in simplified form.

algebra
Volume of a Box A box is constructed by cutting out square corners of a rectangular piece of cardboard and folding up the sides. If the cutout corners have sides with length x, then the volume of the box is given by the polynomial A box is constructed from a square piece of ...

algebra
Like Terms and Degree Identify the degree of each term of each polynomial. Then find the degree of the polynomial xy^3 + 7x^3y^2 - 6xy^4 + 2

Algebra
P dollars is invested at annual interest rate r for 1year If the interest is compounded semiannually then the polynomial P(1+r/2)^2 represents the value of the investment after 1 year. rewrite the expressions without parentheses evaluate the polynomial if P=5670 and r=3.5%

Polynomials
P dollars is invested at annual interest rate r for 1year If the interest is compounded semiannually then the polynomial P(1+r/2)^2 represents the value of the investment after 1 year. rewrite the expressions without parentheses evaluate the polynomial if P=5670 and r=3.5%

POLYNOMIALS
The cubic polynomial f(x) is such that the coefficient of x^3 is -1. and the roots of the equation f(x) = 0 are 1, 2 and k. Given that f(x)has a remainder of 8 when divided by (x-3), find the value of k. okay, this is what i did: -x^3 + bx^2 + cx + d = (x-1)(x-2)(x-k) f(3)=8 -...

pre cal
Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all the real zeros of the function. x^3 - 28x - 48 = 0 Value of x = -4 Please help!!Thank you

Math
Suppose you have a graph of a polynomial function and you can see that the function increases without bound on both left and right ends, has 4 real zereos and has 5 turning points. Based on this information, what is the minimum degree of the polynomial?

pre-calculus
form a polynomial f(x) with real coefficients having the given degree and zeros. degree: 4; zeros: -1, 2, and 1-2i. I got an exam tomorrow, i would appreciate any kind of help, thank you.

*re-Calc
I am trying to get the polynomial; x^7+2x^6+3x^5+4x^4+6x^3+6x^2+7x+8 divided by; x^5-2x^4-3x^3+5x^2+2x-3 into a partial fraction form so that I can create a system of equations to solve for. So far, after dividing I have (x+1)(x-1)^2, and (x^2-x-3) as factors along with an ...

Algebra (College)
I need to divide this polynomial synthetically. I think I did it right, but can someone confirm if my answer is right or wrong? Polynomial: x^4 - x^3 + x^2 - x + 2 Divisor: x-2 My answer: x^3 + x^2 + 3x + 5 + 12 (remainder) ---- x-2

algebra
dividing a polynomial by a polynomial example x-3/x with exponent of 2 -10x+9 or even 2x-3/x with exponent of 2 -10x+9 Thank you any great tutorial sites would help me also.

math
When a polynomial is divided by (x+2), the remainder is -19. When the same polynomial is divided by (x-1), the remainder is 2. Determine the remainder when the polynomial is divided by (x-1)(x+2).

Math
consider the polynomial (x-a)(x-b) and the real number line In each of the three subintervals of the line, write the sign of each factor and the sign of the product.For which values does the polynomial possibly change signs?

Algebra
Can someone please explain how to do these problems. 1)write a polynomial function of least degree with intregal coefficients whose zeros include 4 and 2i. 2)list all of the possible rational zeros of f(x)= 3x^3-2x^2+7x+6. 3)Find all of the rational zeros of f(x)= 4x^3-3x^2-...

Can you please give a example so that I can understand it better. 1)How can you tell whether a polynomial is written in factor form. 2)Construct a trinomial whose greatest common factor is 2x^2.

Math
Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all the real zeros of the function. x^3 - 28x - 48 = 0 x=2 I have no idea how to start this problem!!

Music
What musical form preceded the sonata-allegro form, and is the sonata-allegro form still being used today? Sup' Christy, I beleive the form that preceed the sonata-allegro form would be the "minuet and trio" form. Symphonies are where you can find the s-a form. Laters.

Math
Determine whether the following statement makes sense or does not make sense, and explain your reasoning: When I'm trying to determine end behavior, it's the coefficient of the leading term of a polynomial function that I should inspect. A) This makes sense because the ...

pre-calc
I am trying to get the polynomial; x^7+2x^6+3x^5+4x^4+6x^3+6x^2+7x+8 divided by; x^5-2x^4-3x^3+5x^2+2x-3 into a partial fraction form so that I can create a system of equations to solve for. So far, after dividing I have (x+1)(x-1)^2, and (x^2-x-3) as factors along with an ...

Precalculus
There is at least one polynomial with real functions with 9+i as its only nonreal zero. A. The statement is​ false, because the Fundamental Theorem of Algebra dictates that there must be n complex zeros for a polynomial of degree n.   B.The statement is true. If 9 plus ...

algebra
A polynomial f(x) of degree 3 leaves a remainder of 6 when divided by (x+1) and a remainder of 12 when divided by (x-2). Given that the coefficient of x^3 is 2 and (x+2) is the factor of the polynomial. Show that f(x)= 2x^3+3x^2-5x+2

What polynomial could you subtract from 5x^3 - 12x - x^2 + 9 - 12x^5 - 6x^4 to give a difference of 19 + 8x^3 - 18x - 19x^5 - 2x^2 - 8x^4? Is the answer k (the polynomial) = 7x^5 + 2x^4 - 3x^3 + x^2 + 6x - 28?

algebra
Determine whether each expression is a polynomial. If it is a polynomial, find the degree and determine whether it is a monomial, binomial, or trinomial. 1. 7a^2b + 3b^2 – a^2b 2. 6g^2h^3k

Math--polynomial equation
Write a polynomial equation with these roots. a)-1,2+ã3,2-ã 3 b)2,5,1

algebra 1
Can someone solve theses for me? Factor the polynomial x2 + 7x + 12 completely Factor the polynomial x2 – 4 completely Factor the polynomial 18a2b – 4ab + 10a completely x2 + 7x + 12 = (x+4)(x+3) x2 – 4 = (x+2)(x-2) 18a2b – 4ab + 10a = 2a(9ab - 2b + 5)

Write the polynomial in simplest form with roots 4, 5i and -5i(multiply it out so no parentheses remain (x-4)(x+5i)(x-5i)(NOT SURE ABOUT THIS ONE) (x-4)(x^2-25i^22) (x-4)(x^2+25) x^3+25x-4x^2-100 x^3-4x^2+25x-100 Is this correct

Math - Int Trig
Form a polynomial f(x) with real coefficients having the given degree and zeros 21) Degree: 4, zeroes: 2i and -3i 22) Degree: 3, Zeroes i and -10

algebra
A cylinder has a radius of 4x + 2 and a height of 5x + 4. Which polynomial in standard form best describes the total volume of the cylinder? Use the formula v = pi r^2 h for the volume of a cylinder.

Math--polynomial equation
Write a polynomial equation with these roots. a)-1,2+sqt3,2-sqt3 b)2,5,1 sqt= square root

algebra
Identify the degree of each term of each polynomial. Then find the degree of the polynomial combine like term. m^3+ 2m^2n-3m^2+3ma^2

Algebra 2
The lenths of the side of a triangle are x+4 units, x units, and x+1 units. Express the perimeter of the triangle as a polynomial in standard form.

A polynomial of degree 4 that increases the y-axis at 6 and whose y-values get more and more negative as x -> +infinity and x -> -infinity -Represent a function that satisfies the given conditions by an equation. Leave in factored form.

The polynomial function defined by f(x) = 1 − x + x^2 − x^3 + ... + x^16 − x^17 may be written in the form f(y) = a_0 + a_1 y + a_2 y^2 + ... + a_16 y^16 + a_17 y^17, where y = x + 1 and a_i s are constants. Find a_2.

A polynomial of degree 4 that increases the y-axis at 6 and whose y-values get more and more negative as x -> +infinity and x -> -infinity -Represent a function that satisfies the given conditions by an equation. Leave in factored form.

Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all the real zeros of the function. x^3 - 28x - 48 = 0 Value of x = -4 Please help!!Thank you

Algebra
What type of polynomial is this? 2 - 5x^3 + 6x A)not a polynomial B)cubic trinomial C)quadric trinomial D)fourth-degree trinomial Since the degree is 4, I think the answer is D. Is this correct?

Pre Calculus
How are the factors of a polynomial related to the x-intercepts of a polynomial? How do you find the x-intercepts given the factors?

MATH
if alpha and beta are zeroes of the polynomial x2-5x+6,then find the polynomial whose zeroes are root 3 and -root 3

math
compouned semiannually P dollars is invested at annual rate. r for 1 year. If the intrest is compounded semiannually then the polynomial P(1+r/2)by the second power represent the value of the investment after 1 year. Rewrite this expression without parentheses. Evaluate the ...

Math
John wants to hire an editor to check his thesis paper. The editor charges a flat rate of $50 and$2 per page. Write a polynomial to describe the cost. Find the cost of editing 75 pages. Calculations: Answer: Polynomial: ____________________Cost:_________________

math
n a triange the longest side is 2 more than the shortest side. the third side is half of the sum of the longest side, then express the perimeter in polynomial form

college algebra
form a polynomial f (x) with real coefficients having the given degree and zeros. degree 5; zeros 5; -i; -6+-i f(x)= a(?) Please show step by step work.