4. For the function f(x) x+ 8x + 5x2-38x + 24, use long division to determine whether each of the following is a factor of f(x). a) x + 6 b) x + 1 c) x- 4

Q: Use synthetic division to perform the division.   x^3+5x^2+8x+6 over x+3

A:

Q: Evaluate at the given value using synthetic division. f (x) = x + 8x2 + 15x +3 at x = -3 f(-3)

A:

Q: 24. Use the Factor Theorem to determine whether x – c is - a factor of f (x). f (x) = x* – 5x2 – 36…

A: Given, fx=x4-5x2-36  ;        x-3

Q: USE the synthetic method of division to divide the polynomial f(x) = r" – 32 by d(r) -2.

A:

Q: If a polynomial f(x) when divided by (x – a) gives a remainder r1, and when divided by ( – b) gives…

A:

Q: When a polynomial function f is divided by x - c, theremainder is_______

A: Give a polynomial function f is divided by x - c

Q: Use synthetic division and the remainder theorem to find the indicated function value. f(x) = 4x3 -…

A:

Q: show f(x)=x^3-x^2-8x+12 has no zero greater than 4 and no zero less than -4 using synthetic division

A:

Q: Given that 5 is a zero of f(x) = 3x - 17x + 5x + 25, factor f(x) completely. %3D f (x) = %3D

A:

Q: Prove that x- 3 is a factor of the polynomial x + 4x-17x2-14x + 6 without referring to the graph.

A:

Q: Use an appropriate Chebyshev polynomial to economise f(x) = x³ + 2x² – 5 once

A: In this question, we need to economize the polynomial by using appropriate Chebyshev Polynomial the…

Q: Test the polynomial x – 2x3 + 6x – 3 for irreducibility over Q.

A: We have to check whether the polynomial x4-2x3+6x-3 is irreducible over the set of rational numbers…

Q: 5. Use synthetic division and the remainder theorem to find f(-2) when f(x) = 4x - 9x + 8x2 - 10.…

A:

Q: Use synthetic division and the Remainder Theorem to find the indicated function value:  f(x) = 2x4 -…

A: Given function f(x)=2x4-5x3-x2+3x+2              ...(1)

Q: Use synthetic division and the remainder theorem to find the indicated function value. f(x) = 4x -…

A: Let the function is f(x)=4x2-2x2-7x+3

Q: Use synthetic division to show that f(x) = x³ + 3x² – 13x – 15 is divisible by the linear factor x +…

A: Given query is to use synthetic division on f(x) , and find its factors.

Q: Prove that (x+2) is a factor of 3x'+8x+x-6 and find the other factor.

A: we have to find factor of the polinomial

Q: For the remainder of the division of x-2x²+3kx+18 by x-6 to be equal to zero, k must be equal to?

A:

Q: express f(x) =x³+2x²-x-3 , in term of lagendre polynomial

A: To express the given function f(x)=x3 +2x2 -x-3 in terms of Lagendre polynomial.

Q: Use synthetic division to divide fx) = x – 4x² + x + 6 by x + 1. Use the result to find all zeros of…

A: given,        fx=x3-4x2+x+6       ,   x=-1

Q: The ________ Theorem states that if a polynomial f(x) is divided by x − k, then the remainder is r =…

A: The ________ Theorem states that if a polynomial f(x) is divided by x − k, then the remainder is r =…

Q: 1. Use synthetic division to show that c = 2 is a zero of P (x) = x' – 9x + 10 and then find all the…

A: If c= 2 is a zero of the given polynomial P(x), then after synthetic division we will get reminder…

Q: 9 Use the factorization theorem to determine whether x−1/2 is a factorof f(x) = 2x^4 − x^3 + 2x − 1.

A:

Q: Q3: Factorize f (x) = 2x* + x³ + 2x + 4 € Z5[x] as a polynomials product to irreducible over Z5?

A:

Q: Use synthetic division to show that (x+6) is a factor of f(x) = 2x^3 + 11x^2 -21x – 90, show all…

A:

Q: For f(x)=2x4 +2x3-1 and g(x)=2x3 +2x+3 in Z4[x], the degree of fg is 7. True or false

A:

Q: Use the Intermediate Value Theorem to show that the given polynomial f(x) = 3x3 - 8x2 + x + 2 has a…

A: Given- fx=3x3-8x2+x+2 To show-  that the given polynomial has a real zero between the given integers…

Q: Evaluate when x = -3 by using the Remainder Theorem. 35. f(x)=x-5x² +6x-3

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

Q: 1.  if the result of a polynomial division is 2x3 - 4x2 - 5x +23/x+2,   make at least three…

A: Given that the result of a polynomial division is 2x3-4x2-5x+23x+2. It is required to make at least…

Q: If a polynomial f(x) has a remainder of -9 when divided by a 3, what is f(3)?

A:

Q: Gives that f(x) 5x^3-54x^2+170x-104. And that 5+i is a zero, factor f(x) completely.

A: If 5+i is a zero then (5-i) is also a zero.

Q: 1 Use synthetic division to decide whether is a zero of f(x) = 25x* + 24x2 + 15x +2. - - 1 Is a zero…

A: The given function can be written as f(x)=25x4+0.x3+24x2+15x+2

Q: Is x+ 4 a factor of f(x) = x5 + 10x4 + 29x3 – 28x2 (Use Synthetic Division in conjunction with the…

A:

Q: Use synthetic division and the Remainder Theorem to find the indicated function value.…

A:

Q: 3. Find algebraically the zeros for f (x) = x - 4x 9x + 36x %3D

A: Given function

Q: 5. Use the Intermediate Value Theorem to show that f(x) = 3x³ – 10x + 9 has a real zero between -3…

A:

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

A:

Q: #7: For what value of k will the polynomial function f(x)=x'+6x² +kx=4 have the same remainder when…

A: The Polynomial Remainder theorem states that if x-b divides the polynomial, Qx, then the remainder…

Q: Evaluate at the given value using synthetic division. f (x) = x+ 8x2 + 15x +3 at x = -3 f(-3)

A: f(x) = x3 +8x2 +15x +3

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

A:

Q: 8. Find the sum of all the zeros of the polynomial f(x) = x + 2x2-5x-6 O -5 -2 0. 2 6

A: Given equation is fx = x3+2x2-5x-6Comparing it with ax3+bx2+cx+d = 0a = 1, b = 2, c = -5, d = -6

Q: Evaluate when x = 1 by using the Remainder Theorem. 31. f(x)=x -5x² +6x- 3 32. g(x)=2x –3x² +5x+3…

A:

Q: Use the Factor Theorem to show that the statement in the exercise is true.

A:

Q: Use synthetic division and the remainder theorem to find the indicated function value. f(x) = 4x -…

A:

Q: 23 2. If the result of a polynomial division is 2x3 – 4x2 – 5x + x + 2 make at least three…

A: The result of the polynomial division is, 2x3-4x2-5x+23x+2 Let, f(x)=2x3-4x2-5x+23x+2…

Q: if the sum of the zeroes of the polynomial f(x) = 2x³ – 3kx² + 4x - 5 is 6, then the value of k is

A:

Q: Use synthetic division and the Remainder Theorem to find the indicated function value. f(x) = 3x-20x…

A: We will use synthetic division and remainder theorem to answer the given question.

Q: Find Ao, A1, and 4, in rewriting the function of ()- r>0 in terms of Lagure polynomial, /)=4L(*).

A:

Q: 3 Use synthetic division to divide f(x) =x° + 18x + 101x+ 180 by x+4. Use the result to find all…

A:

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…

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.