# 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

60,820 results
1. ## Alegbra 2

Use the rational root theorem to list all possible rational roots for the equation. X^3+2x-9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x-6=0. A polynomial function P(x) with rational coefficients has the

2. ## 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

3. ## 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

4. ## 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 4-sqrt 6

5. ## Pre-Calc

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.

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

7. ## pre-calc

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)= 5-x^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.

8. ## calculus

1.is the function f(X)=4-7x^5 a polynomial function? if so state its degree and leading coefficient. 6.use the remainder theorem to determine if x-2 is a factor of the polynomial f(x)=3x^5-7x^3-11x^2+2

9. ## 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).

10. ## 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

11. ## 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

12. ## Algebra

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

13. ## Algebra

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

14. ## 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

15. ## Algebra

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

16. ## Pre Calc

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. f(x)=-3x^3-3x^2-2x+1 ?????????????

17. ## Math-college

Find an​ nth-degree 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.

18. ## math

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

19. ## 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

20. ## 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^5-20x^4 B) -8x^5+10x^4 C) -7x+2x^4 D) -7x^5-10x^4 3. Consider the leading term of the

21. ## 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

22. ## Algebra

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

23. ## 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

24. ## pre-ap 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

25. ## 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.

26. ## 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

27. ## Algebra 2

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

28. ## 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)

29. ## 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

30. ## Math

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

31. ## 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

32. ## Algebra II

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

33. ## Algebra

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

34. ## 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!

35. ## 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

36. ## Algebra

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

37. ## 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

38. ## 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)

39. ## Algebra 2

Find a third-degree polynomial equation with rational coefficients that has roots -1 and i+1

40. ## 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!

41. ## algebra

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

42. ## 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.

43. ## ALGEBRA

Find a degree 3 polynomial with real coefficients having zeros 2 and 4-3i and a lead coefficient of 1.

44. ## 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

45. ## 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.

46. ## algebra

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

47. ## pre-calculus 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

48. ## precalc

find the rational expression R whose numerator and denominator have degree 2 and leading coefficients of 1 such that (x^2 + 3x-10)/(x^2 -8x+15) * R = (x-2)/(x-3)

49. ## 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)

50. ## 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 ) .

51. ## 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

52. ## Math

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

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

54. ## 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

55. ## 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!

56. ## 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..

57. ## 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)(x-2) should be given

58. ## 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

59. ## AMath

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

60. ## Algebra

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

61. ## Algebra

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

62. ## 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.

63. ## Pre-calc

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)

64. ## algebra

1)A.f(x)= x^2+4 B.f(x)= x^2-4x^2+4x-16 C.f(x)= x^2+4x^2+4x+16 D.f(x)= x^2-4x^2-4x+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

65. ## 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

66. ## 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

67. ## 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.

68. ## 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

69. ## Pre Calculus

1. Find all rational zeros of the polynomial. Then determine any irrational zeros, and factor the polynomial completely. 3x^4-11x^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

70. ## 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!

71. ## algebra

Choose the best response to descrive the polynomial. -4x^3-2x^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!

72. ## 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

73. ## 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.

74. ## math

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

75. ## Math-precalc

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

76. ## 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

77. ## Math

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

78. ## Algebra

Find the real zeroes of the polynomial: f(x)=2x(x+5)^2-8x 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}

79. ## 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

80. ## 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

81. ## 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

82. ## 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

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

84. ## Algebra

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

85. ## 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

86. ## 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

87. ## Algebra

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

88. ## Math

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

89. ## algebra

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

90. ## math

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

91. ## 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

92. ## MATH

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

93. ## 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

94. ## Math

(a) Consider the improper function f(x)= (x^4+x^3+2x^2+x-1)/(x^3-x^2+x-1). Use long division to convert f(x) into a polynomial plus a proper rational function. -->I ended up with : (x+2) + (3x^2-2x-3)/(x^3-x^2+x-1) (b) Factor the polynomial Q(x) = x^3 -

95. ## 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

96. ## 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+ .

97. ## 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 .

98. ## 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

99. ## 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

100. ## Math - polynomial function

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