Answered: Use long division to find a value of k…

Use long division to find a value of k such that f(x) is divisible by d(x). f(x) = x4 + x3 + 3x² + kx – 4; d(x) = x² – 1

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter5: Factoring Polynomials

Section5.7: Factoring Pattern For X2+bx+c, C Positive

Problem 44WE

See similar textbooks

Related questions

Q: Consider the polynomial h with h"(x)=(x-5)^3(x-3)^2 Use the definition of an inflection point to…

Q: Find a polynomial f(x) of degree 4 with real coefficients and the following zeros. -1 (multiplicity…

A: See attached file for a step by step explanation.

Q: The general polynomial of degree n has the form P(x) = an xn + an-1 xn-1 + ........ + a2 x2 + a1 x +…

A: Consider the general form polynomial of degree n which is shown below,

Q: The general polynomial of degree n has the formP(x) = an xn + an-1 xn-1 + g + a2 x2 + a1 x + a0where…

A: Consider the general form polynomial of degree n P(x)=anxn+an-1xn-1+....+a2x2+a1x+a0

Q: Find a polynomial P(x)=x3+ax2+bx+c satisfying ALL of the following properties:

Q: Find a polynomial function f of degree 4 whose coefficients are real numbers that has the zeros…

A: Given: Zeros of polynomials are 1,1,and -4+i.

Q: Find the remainder when f(x) = x7 + 3x5 + x - 1 is divided by x2 +1 in Z5[x].

Q: 4 Let p(x) be a degree 3 polynomial with a negative leading coefficient. Which of the functions…

A: p(x) be a polynomial of 3 degree with negative leading coefficient.

Q: Find a polynomial f(x) of degree 4 that has the following zeros. 1,-7,0,2 Leave your answer in…

A: The objective is to find the polynomial of degree 4. If a is the zero of any polynomial f(x), then…

Q: Find a polynomial f(x) of degree 3 that has the following zeros. 5, 1, -6

Q: Let f(x) be a polynomial with real coefficients. The polynomial f(x) leaves the remainder 2x +1 when…

Q: Consider the polynomial h with h' (x) = (x – 5)³(x – 3)². Use the definition of an inflection point…

A: We will solve the problem.

Q: Find a polynomial function with real coefficients that has the given zeros: 1,1, 2+√3i.

Q: 2. Use the Remainder Theorem to find each function value below: f(x) = x³ – 2x4 +x³ + 3x – 8 (a)…

A: According to remainder theorem, when a polynomial f(x) is divided by a linear polynomial (x-a) then…

Q: Analyze the polynomial function f(x) =x-(x- 2) using parts (a) through (e).

A: Please find attachment for the details solution

Q: Use the remainder theorem to find f (c).

A: Given function is fx=x4-6x2+4x-8.

Q: Find the upper and lower bounds of the zeroes of each polynomial function. 1. f(x) = x^3 + 4x^2 + 8x…

Q: Use long division and express P in the form P(x) = D(x) · Q(x) + R(x). P(x) = 20x4 + 16x3 + 9x2,…

A: Explanation: Given that, P(x) = 20x4 + 16x3 + 9x2, D(x) = 4x2 + 1 We will follow some steps to…

Q: Find a polynomial of degree 3 that has zeros of 3,-4, and 5, and where the coefficient of x2 is 8. O…

A: Given that the zeros are 3, -4 and 5. So the factors of the polynomial is (x-3), (x+4) and (x-5)…

Q: Use the remainder theorem to find the remainder when f(x) is divided byx-C. f(x) =x* +8x + 12x; x+1

Q: 6. Use the Remainder Theorem to evaluate f(x) = 10x* - x3 + 13x2 – 9x + 17 at x =-.

A: Since the student has mentioned to solve question number (6), so we are solving only question number…

Q: 3. Which of the following polynomial function has degree = 3 and leading coefficient -6? a)…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Find the asymptotes of the functionf(x)=x2−3x+2 / x2+3x+2.

A: We factor the numerator and the denominator. Then we set the denominator equal to 0 to find the…

Q: 6. Use the Remainder Theorem to find f(-1/3) if f(x) = 6x5 - x4 + 11x3 - x + 51

Q: Write a polynomial f(x) of degree 3 given zeros 4and 5i. f(x) = x + 4x²? +25x + 100 %3D O f(z) = x -…

A: Zeros of fx are 4 and 5i. Since complex roots occur in conjugate pairs, therefore -5i is also the…

Q: 10 h(x) = x³ + 5x² - 4x- 20 %D

Q: long division

Q: Find a polynomial of degree four that has zeros -3, 0, 1, and 5, and the coefficient of x3 is -6.

A: We need to find a polynomial of degree four that has zeros -3, 0, 1, and 5, and the coefficient of…

Q: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. 3, 4i

Q: 2. D- f(x) = -is not a polynomial function because %3D 2x

A: A polynomial function is a function such as a quadratic, a cubic, a quartic, and so on, involving…

Q: Find m so that x– 5 is a factor of f (x)= 4x² – 21x² +mx–15.

A: Consider the given polynomial fx=4x3-21x2+mx-15

Q: 4. Use synthetic division to show that c is a zero of the given polynomial function. a. P(x) =x'-4x²…

Q: Use the remainder theorem to find f (c).

A: The function fx=2x3+4x2-3x-1 & c=3

Q: Consider the polynomial h with h'(x) = (x – 5)³(x– 3)². %3D Use the definition of an inflection…

A: we know that a point of inflection is found where the graph of a function changes concavity. To find…

Q: Use the remainder theorem to find f (c).

A: Given: f(x) = x4+3x2-12, c = -2 To find: Value of f(c) using remainder theorem.

Q: Find the zero(s) of the polynomial ³ - x²-3x+3.

Q: Find a polynomial function of degree 3 that has zeros 1, -2, and 3 and in which the coefficient of x…

A: We need to find the a polynomial function of degree 3 that has zeros 1, -2, and 3 and in which the…

Q: Let f(x) = 5x4 + 3x3 + 1 and g(x) =3x2 + 2x + 1 in Z7[x]. Determine the quotient and the remainder…

Q: IV. Use the factor theorem to show that d(x) is a factor of f(x).

A: Factor theorem :If f(c)=0 then x-c is a factor of f(x) or if x-c is a factor of f(x) then f(c) = 0

Q: 4. How should the polynomial function f(x) = -x + 2x³ + 3x5 – 6 be written in standard form? A. f(x)…

Q: Use the remainder theorem to find the remainder when f(x) is divided by the given x−k.…

Q: 4. Use synthetic division to show that c is a zero of the given polynomial function. b. P(x) =2x³ –…

A: Solution is given below:

Q: f(x) = x + 5x3 - 7x2-29x + 30 %3D

Q: Use synthetic division to show that c is a: a. P(x)=x'-4x² + 5x – 2; c = 2

Q: Find a polynomial f (x) of degree 3 that has the following zeros. 0, 5, -8

A: Given problem is :

Q: Find the Maclaurin polynomials po(x), p1(x), and p2(x) for f(x) = e' -4x. (show all necessary…

A: As we know that the Maclaurin series of ex is simple So we are going to use the Maclaurin series of…

Q: Find a polynomial f (x) of degree 4 that has the following zeros. -4, 1, -9, 0 Leave your answer in…

A: Polynomial with zeros -4,1,-9,0 can be written as below :

Q: Find the critical points, A and B, of the following polynomial (with A<B) f(x) = 6x3 - 45x2 - 432x…

A: A = -3.04 B = 8.04

Q: Use synthetic division to show that c is a zero of f (x) .

A: Given: fx=4x3-9x2-8x-3; c=3 Write the problem in a division-like format. To do this: Take the…

Question

How do I solve this?

Use long division to find a value of k such that f(x) is divisible by d(x).
f(x) = x4 + x3 + 3x² + kx – 4;
d(x) = x² – 1
k =

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find a fourth-degree polynomial function f with real coefficients that has 2, 2, and 7i as zeros.
If we divide the polynomial P by the factor xc and we obtain the equation P(x)=(xc)Q(x)+R(x) , then we say that xc is the divisor, Q(x) is the ______, and R(x) is _______.
Use the Remainder Theorem to find the remainder when f(x)=x37x+12 is divided by x+3 .
A polynomial of degree n I has exactly ____________________zero if a zero of multiplicity m is counted m times.