Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. 1) 2, 1, 1 2) i, 4 3) i, 2  √3 4) 1, 4, 1 + √2
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Alegbra 2
Use the rational root theorem to list all possible rational roots for the equation. X^3+2x9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x6=0. A polynomial function P(x) with rational coefficients has the

Precalculus
Suppose that a polynomial function of degree 4 with rational coefficients has i and (3 + square root of 3)as zeros find the other zeros

PreCalculus
Suppose that a polynomial function of degree 5 with rational coefficients has the given numbers as zeros. Find the other zero( s): 1, radical 3, 11/3

Algebra 2
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros 2, 2i, and 4sqrt 6

PreCalc
A polynomial function f(x) with real coefficients has the given degree, zeros, and solution point. Degree: 3 Zeros: 2,2+2√2i Solution Point: f(−1) = −68 (a) Write the function in completely factored form. (b) Write the function in polynomial form.

Math Help Please
Suppose that a polynomial function of degree 5 with rational coefficients has 0 (with multiplicity 2), 3, and 1 –2i as zeros. Find the remaining zero. A. –2 B. –1 – 2i C. 0 D. 1 + 2i

precalc
1. which of the following is a fourth degree polynomial function? select all that apply. a. f(x)= 4x^3  x^2 + 2x  7 b. f(x)= 5x^4 c. f(x)= 1 / 2x^4 + x^2 5 d. f(x)= 3x^4 + 2x^3 4x +1 2. which function below has the end behavior f(x) approaches neg.

calculus
1.is the function f(X)=47x^5 a polynomial function? if so state its degree and leading coefficient. 6.use the remainder theorem to determine if x2 is a factor of the polynomial f(x)=3x^57x^311x^2+2

precalc
The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=3 and x=0 , and a root of multiplicity 1 at x=− 2, find a possible formula for P(x).

algebra
HELP!!!!!!!!!!!!! write equation of a polynomial function with the given characteristics. Leading coefficient is 1 or 1 crosses the x axis at 2,3, and 4 touches the x axis at 0 lies above the x axis between 2 and 0

Math
Which of the following statements about a polynomial function is false? 1) A polynomial function of degree n has at most n turning points. 2) A polynomial function of degree n may have up to n distinct zeros. 3) A polynomial function of odd degree may have

Algebra
Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 3i,sqrt2 f(x)=??

Algebra
Form a third degree polynomial function with real coefficients such that 7 + i and 9 are zeros

Algebra 2
How would you write a polynomial function with rational coefficients so that P(x)=0 has the given roots? The given roots are 2,2,3,5

Algebra
Find the polynomial function P of the lowest possible degree, having real coefficients, with the given zeros. 3+2i, 2 and 1

Pre Calc
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. f(x)=3x^33x^22x+1 ?????????????

Mathcollege
Find an nthdegree polynomial function with real coefficients satisfying the given conditions. n=4; i and 3 i are zero; f(2)=65 f(x)= An expression using x as the variable. Simplify your answer.

math
third degree with zeros of 2i,2+i and 2 and a leading coefficient of 4. Construct a polynomial function with stated properties

Math
What does the degree of a polynomial expression tell you about its related polynomial function? Explain your thinking. Give an example of a polynomial expression of degree three. Provide information regarding the graph and zeros of the related polynomial

Algebra
HELP ALGEBRA HOMEWORK 1. Classify 6x^5+4x^3+3x^2+11 by its degree. A) quinic B) cubic C) quartic D) quadratic 2. Write 2x^2(5x2+4x^3) in standard form. A) 8x^520x^4 B) 8x^5+10x^4 C) 7x+2x^4 D) 7x^510x^4 3. Consider the leading term of the

poloynomial function
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. 1) 2, 1, 1 2) i, 4 3) i, 2  √3 4) 1, 4, 1 + √2

Algebra
Given these zeros, write a polynomial function of least degree with integral coefficients. 2i, 2 + 2.236

mathematics
Find a polynomial function P of the lowest possible degree, having real coefficients, a leading coefficient of 1, and with the given zeros. 2plus2i, minus1, and 2

preap Algebra 2
write a polynomial function f of least degree that has the rational coefficients, a leading coefficient of 1, and the given zeros. Given zeros: 2,2,1,3, sqrt 11

pre calc
A polynomial f(x) with real coefficients and leading coefficient 1 has zeros 6 + 4i, 5 + i and degree 4. Express f(x) as a product of quadratic polynomials with real coefficients that are irreducible over R. ive done this problem every which way i could.

math
Form a polynomial f(x) with real coefficients, with leading coefficient 1, having the given degree and zeros. Degree: 4; zeros: 4+3i and 1; multiplicity of 2

Algebra 2
write a polynomial function of least degree with integral coefficients whose zeros include 4 and 2i

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)

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^32x^2+7x+6. 3)Find all of the rational zeros

Math
A polynomial function with rational coefficients has the following zeros. Find all additional zeros. 2, 2 + ã10

algebra 2
write a polynomial function of least degree that has real coefficeints the given zeros and a leading coefficient of 1. the problem is 5,2i,2i

Algebra II
write a fourth degree polynomial function a leading coefficient o 1 given three of its zeros are 1, 3 and 2i, then rewrite it in simplified form.

Algebra
Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 2i,sqrt2 f(x)= ? Thanks!

Algebra
Write a polynomial of least degree with real coefficients and with the root 68i. Write your answer using the variable x and in standard form with a leading coefficient of 1. Thanks, I have no idea!

pre cal
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 3, 13, and 5 + 4i Urgently need help

Algebra
Write the polynomial in descending order. Then identify the leading coefficient and the degree. 2x+8+2x4 Need HELP

Precalculus
Suppose that a polynomial function of degree 4 with rational coefficients has i and (3 + square root of 3)as zeros find the other zeros show work please

algebra
write a fourth degree polynomial function with real coefficients that has 3,1/5, and 4+i as zeros and the y intercept of (0,5)

Algebra 2
Find a thirddegree polynomial equation with rational coefficients that has roots 1 and i+1

Algebra
Suppose that a polynomial function of degree 5 with rational coefficients has 6, −2+4i, 4−sqrt2 as zeros. Find the other zeros. Thank you!

algebra
A cubic polynomial function f(x) has leading coefficient 2 and intercepts the yaxis at 2. If f(1)=1, and f(2)=2, find f(1) and write the complete function.

math =(
Sketch a graph of a polynomial function that is degree 5 with all real zeros, a positive leading coefficient, one negative zero, and two positive zeros.

ALGEBRA
Find a degree 3 polynomial with real coefficients having zeros 2 and 43i and a lead coefficient of 1.

Math Help? Check my answers.
1. Name the coefficients in the polynomial. 4x^2 + 3x  3 4, 3, 3 4, 3, 4, 3, 3, 4, 3, 2. How many terms are in the following polynomial? 6x^4 + 3x^3  2x^2 + 15x  14 5 4 3 2 3. In the expression 7x  5x^2 + 5, what is the coefficient of x? 7 5 5 7

algebra 2
Write a polynomial function that has the zeros 2, 2, and 1 and has a leading coefficient of 1. Then graph the function to show that 2, 2, and 1 are solutions.

algebra
Find a polynomial function of least degree with real coefficients satisfying the given properties. zeros 3, 0, and 4 f(1) =10

precalculus math
A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over . 3, −3 − 2i; degree 3

precalc
find the rational expression R whose numerator and denominator have degree 2 and leading coefficients of 1 such that (x^2 + 3x10)/(x^2 8x+15) * R = (x2)/(x3)

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)

Math
The polynomial of degree 5, P ( x ) has leading coefficient 1, has roots of multiplicity 2 at x = 4 and x = 0 , and a root of multiplicity 1 at x = − 1 Find a possible formula for P ( x ) .

Math
True or false Some rational numbers are integers. The radius of a circle and its circumference. Direct or inverse f(x) 0.08x^3 + 0.6x + 2.8 Rational function, another polynomial function Quadratic function

Math
1. Identify the degree, leading term and leading coefficient of each polynomial function. A. f(x)= x(x+1)(3x+1)(x2) B. f(x)= 16+3x^4  9x^2  x^6 + 4x^8 2. Describe the end behavior of a ninthdegree polynomial function with a negative leading

algebra!!!! please help me!!!!
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

Algebra
Suppose that a polynomial function of degree 5 with rational coefficients has 0 (with multiplicity 2), 6, and –2 + 3i as zeros. Find the remaining zero. A. –6 B. –2 – 3i C. 0 D. 2 + 3i

Algebra
Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. sqrt of 3 and 4i disregard the first post, thanks!

math 8
how do the degree and the sign of the leading coefficient correspond to the end behaviour of the polynomial function. please help I don't know where to start..

math
Find a polynomial f(x) with leading coefficient 1 and having the given degree and zeros. Each polynomial should be expanded from factored form, simplified and written in descending order of exponents on the variable. For example: (x+5)(x2) should be given

Math
Hello! I've been having trouble deciding what type of function this equation is: y=√x / x^2+8 There are a couple possbilties to pick from such as; power, root, rational, algebraic, polynomial by degree 2 and polynomial by degree 8. I thought it would be

AMath
Write a polynomial function of minimum degree in standard form with real coefficients whose zeros include those listed 2, 3 and i.

Algebra
Sketch the graph of a polynomial of degree 3 with a positive leading coefficient whose zeros are 4, 2 and 3

Algebra
Form a third degree polynomial function with real coefficients such that 2+i and 5 are zeros. f(x)= ?

Math
Suppose f(x) is a polynomial of degree of 5 and with leading coefficient 2009. Supposdm further that f(1) = 1, f(2) = 3, f(3) = 5, f(4) = 7, f(5) = 9. What is the value of f(6). The answer given in book is 241091. Please work the complete solution.

Precalc
The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=3 and x=0, and a root of multiplicity 1 at x=5 Find a possible formula for P(x)

algebra
1)A.f(x)= x^2+4 B.f(x)= x^24x^2+4x16 C.f(x)= x^2+4x^2+4x+16 D.f(x)= x^24x^24x+16 2)A.+1,+2,+3,+6 B.0,+1,+2,+3,+6,+1/3,+2/3 C.+1,+2,+3,+6,+1/3,+2/3 D.+1,+3,+1/6,+1/3,+1/2,+3/2 4)I don't know what they mean either but this is all it

mathematics
1. How many real roots does y=x^3+x^2+9x+9 have? 2. If you know that a 6th degree polynomial has at least 5 complex roots, how many complex roots does it have in total? 3. A polynomial function has 3 real roots and 4 complex roots. What is the degree of

Math
Can someone help me with these T.T 1.Which polynomial function would have the end behaviour of as x> ∞, y= +inf and as x> ∞, y> ∞? a) f(x) = 6x^4  x^5 + 5x^3  x^2  4x + 9 b)f(x)= 6x^4 + x^5  5x^3 + x^2 + 4x  9 c)f(x) = 3x^2 + x  11

Math
Some rational numbers are integers. True or false The radius of a circle and its circumference. Direct or inverse f(x) 0.08x^3 + 0.6x + 2.8 Rational function, another polynomial function Quadratic function.

Writing polynomial functions
How to write a polynomial function with the integral coefficients that have the following roots: #1.) 0, 1/2, 6 #2.) + or  5i

Pre Calculus
1. Find all rational zeros of the polynomial. Then determine any irrational zeros, and factor the polynomial completely. 3x^411x^3+5x^2+3x 2. Find the polynomial with leading coefficient 1 that has a degree of 4, a zero of multiplicity 2 at x=1 and a zero

Algebra
Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. sqrt of 3, 4 Thanks!

algebra
Choose the best response to descrive the polynomial. 4x^32x^2+2x A) The coefficients are all negative B) The leading coefficient is negative C) It is a binomial D) It is of degree four. I was thinking it is c could someone tell me if I am right! Thanks!

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

m240
Determine the degree and the leading coefficient of the polynomial function f(x) = 2x3 (x  1)(x + 5). A. 5; 2 B. 7; 4 C. 2; 5 D. 1; 9 My answer is A is this correct.

math
Given that the range of a polynomial function is {y  y

Mathprecalc
Is it possible to find a rational function that has xintercepts (2,0) and (2,0), but has vertical asymptote x=1 and horizontal asymptote of y=0? The horizontal asymptote and the xintercepts parts stump me. If you can't reach y=0, then how can you get

algebra
file:///C:/Users/Pat/Downloads/IMG_0166.JPG Above is a graph of a polynomial function ƒ with real coefficients. Use graph to answer following questions about ƒ. All local extreme of ƒ are shown on graph. a. the function is decreasing over which

Math
Write a polynomial function in standard form that has the given zeros and has a leading coefficient of 1 for: 2, 4+i

Algebra
Find the real zeroes of the polynomial: f(x)=2x(x+5)^28x I know you can pull the factors from the leading coefficient and the constant: constant = p= 5 factors 1, 5 leading coefficient= q= 2 factors 1, 2 so would my rational zeros be: +/{1, 1/2, 5, 5/2}

Equivalent Algebraic Expressions
The game shown at the right consists of eight pairs of coloured squares called dominos. Rules: 1. Write a polynomial in each square marked P and a rational function in each square marked R. 2. The expressions you write must satisfy each of these

Algebra 2
The Question(s):: Write the polynomial 22x+5x^22x^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 help!
I don't understand my problems that I am suppose to do. please help. Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or 1 and make the degree of the function as small as possible. 1.Crosses the

Writing equation of a polynomial function
Can you help me with the following questions, I don't understand. thanks! Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or 1 and make the degree of the function as small as possible. #1. Crosses

calculusplease help!!
I have two questions that I don't understand and need help with. 1. information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zerosof f. degree 4, zeros i;9+i 2. form a polynomial f(x) with real coefficients

Algebra
Sketch the graph of a polynomial of degree 2 with a leading coefficient of 3 whose zeros are 5 and 1.

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

Algebra 2
1. Write a polynomial in standard form that has solutions: 0, 2, 3 2. Write a trinomial that has a degree of 4 and a lead coefficient of 3 3. True of false: 3/x^2 is a polynomial expression

Algebra
Determine a polynomial function of degree 3 with real coefficients whose zeros are ƒ{2, 1+i .

Math
find a third degree polynomial function with real coefficients 2+i and 4 zeros

algebra
Find an equation of a polynomial function of degree 5 with integer coefficients with zeros 0, 2, and 1/2.

math
Find an equation of a polynomial function of degree 5 with integer coefficients with zeros 0, 2, and 1/2.

algebra 2
Factor completely with respect to the integers. 1. 9x^2  4 2. x^3 + 64 3. 200x^2  50 4. 8x^3  64 5. x^3 + x^2 + x + 1 6. x^3  2x^2 + 4x  8 7. 2x^3 + 4x^2 + 4x + 8 8. 2x^3 + 3x^2 32x  48 9. 7x^3 + 14x^2 + 7x 10. 6x^3  18x^2  2x +6 11. 3x^4  300x^2

MATH
write, in extended form, a polynomial(with real coefficients) of degree 3, with solutions 2,2i.

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

Math
(a) Consider the improper function f(x)= (x^4+x^3+2x^2+x1)/(x^3x^2+x1). Use long division to convert f(x) into a polynomial plus a proper rational function. >I ended up with : (x+2) + (3x^22x3)/(x^3x^2+x1) (b) Factor the polynomial Q(x) = x^3 

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
Create a 3rd degree polynomial with real coefficients that has roots 1 and 4i. Write your answer in form ax^3 + bx^2 + cx+ .

Math
Create a 3rd degree polynomial with real coefficients that has roots 1 and 4i. Write your answer in form ax^3 + bx^2 + cx+ d .

Calculus II
Fed loves polynomials with rational coefficients and only such polynomials.Suppose f(x)=square root of x. Find a polynomial P(x) that Fred will adore so that, for any x in the interval [3,5], the difference between P(x) and f(x) is less than .01 Hint: The

calc
find the values of a nad b if the function f(x)=2x^3 + ax^2 + bx + 36 has a local max when x=4 and a min when x=5 First you calculate the derivative: f'(x)=6x^2 + 2ax + b (1) At the local maximum and minumum f' is zero. If a polynomial is zero at some

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