Let f (x) = 4x³ + ax2 + 5x +b. Find a and b such that x-1 is a factor and dividing f by x+ 2 we get the remainder -57.

Q: Given f(x) = 3x3 + 4x2 - 5x + 3, use the Remainder Theorem to find f(-4).

A:

Q: The polynomial p(x) = 2-(x+1)+x(x+1)- 2x(x+1)(x–1) interpolates the first four points in the table:…

A: Given, the polynomial p(x)=2-(x+1)+x(x+1)-2x(x+1)(x-1)   interpolates the first four points in the…

Q: Find a, b, c E R such that the polynomial f(x) = x³ + ax? + bx + c is divisible by g1(x) = x + 2 and…

A: The remainder theorem says that when a polynomial px is divided by x-a. The remainder is obtained as…

Q: Show that (x- 3) is a factor of 2.x3 - 2x2 - 17x + 15. Hence express 2x³ – 2.x² – 17x + 15 in the…

A:

Q: Consider a polynomial f (x) = ax³ – bx +c. Find the value of b if f' (2) = 0 and fl" (2) =44. -

A: The solution is given in the next step.

Q: What is the remainder when f(x) = - 3x17 + x9 - x5 + 2x is divided by x + 1?

A:

Q: Given f(x) =x3-7x2+5x-6, use the Remainder Theorem to find f(3). %3D

A: The solution for the above question is as shown below.

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

A:

Q: (b) Generalize the remainder theorem to work for lm.d if m 7 0 instead of only l1,-k. In other…

A: b) We want to find the remainder after dividing f by lm,d if m≠0. Where f is a polynomial and lm,d…

Q: 9. For the polynomial f(x) = x(3x + 1)(x – 2)², determine the leading coefficient, leading term,…

A: Given: fx=x3x+1x-22 Now solve the parenthesis we get, ⇒fx=3x4-11x3+8x2+4x                    ...(1)…

Q: Find a, b, c E R such that the polynomial f(x) = x³ + ax? + bx + c is divisible by g1 (x) = x + 2…

A: The given question is related with polynomials. Given that,                  fx = x3 + ax2 + bx + c…

Q: Given f(x) = x3 - 4x2 + 5x + 3, use the Remainder Theorem to find f(2).

A:

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

A:

Q: Use the Remainder Theorem to find the remainder when e ded by the corresponding binomial. 1. x3+2x2+…

A: using remainder theorem to find the remainder when the polynomial divided by corresponding binomial1…

Q: Given f(x) = 2r – 7x + 9x - 3, use the Remainder Theorem to find f(-13). %3D

A: Given: f(x)=2x3-7x2+9x-3, Use the Remainder theorem to find f(-13)

Q: Consider the division f(x) ÷ (x – k) where f(x) = (x + 5)²(x – 5)(x + 6)³. %3D (a) What is the…

A:

Q: Use the Remainder Theorem to find the remainder when f(x) is divided by x-c f(x)= 5x6-3x3+8; x+1

A: The remainder theorem states that whenever polynomial function f(x) is divided by (x− c) the…

Q: Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x) and…

A: We have to find

Q: Consider the polynomial P (x)=kx' + 3x + 4x + 2. 3. 2. %3D Find the value of k such that the…

A: The solution of the problem is given in the next step.

Q: What is the remainder when f(x)= - 3x17 + x9 - x5 + 2x is divided by x + 1?

A: f(x)=-3x17+x9-x5+2x is divided  by x+1

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

A:

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

A: Given that, f(x)=3x3-x2+5x-4

Q: Find the value of p from the polynomial  x2 +3x+p if one of the zeroes of the polynomial is 2

A:

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

A:

Q: Determine the degree of the polynomial P(x) and arrange the terms in decreasing order. 4x3 - 3 +…

A: Polynomial and its Degree.

Q: Use the remainder theorem to find the remainder when f(x) is divided by the given x-k. f) = 32 - Sx…

A: f(x) = 3x2 - 5x + 6 and divisor = x - 2 By using remainder theorem

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: 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: Show that factorial polynomial represent the function: -1+2r – 3r2 + 42 is -1+ (2 – 3h + 4h²)æ(-1) +…

A: Given function, -1+2x-3x2+4x3 To show that the factorial polynomial representation of above function…

Q: Determine the values of m and n for f(x)=mx3+20x2+nx-35 given that (x+1) gives a remainder of zero,…

A: Given that f(x)=mx3+20x2+nx-35 given that (x+1) gives a remainder of zero, and when divided by (x-2)…

Q: The polynomial p(x) has the rest (x+2) when dividing it by (x^2+2x-3) and the rest 1 when dividing…

A: We have given that  p(x) leaves the remainder (x+2) when divided by x2+2x-3 and  p(x) leaves the…

Q: Use the Remainder theorem to find the remainder when f(x) = x3 + 3x? – 18x - 40 is divided by x- 2.…

A: According to reminder theorem, if a polynomial f(x) is divided by (x-a), then the  reminder is the…

Q: n which interval does the polynomial function f ( x ) = x 3 − x 2 − 31 have a zero?

A:

Q: One factor of f(x) = 4x³-4x²-16x+ 16 is (x-2). What are all the roots of the function? Use the…

A:

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

A:

Q: Use the Remainder Theorem to find the remainder when divided by the corresponding binomial. 1. x3 +…

A: As per our guidelines we are supposed to solve only one question

Q: Find the remainder when f(x) is divided by x- k. 3) f(x) =x³ – 13x² + 15x + 14 k =-1

A: follow next step

Q: If f(x) = x* - 3x2 – 2x + 5, use the Remainder Theorem to find f(-2). -2 1 0 -3 -2 5 -2 4 -2 8 1 -2…

A: Solution:Givenf(x)=x4-3x2-2x+5To find f(-2)using remainder theorem

Q: Consider the division f(x) ÷ (x – k) where f(x) = (x + 8)²(x – 8)(x + 5)³. (a) What is the remainder…

A:

Q: find the remainder when the polynomial x^4 - 6x^3 + 4x^2 + 5x +3 is divided by (x + 1)

A:

Q: If 1 is  a zero of the polynomial  p(x) = ax2 - 3 (a - 1 )x - 1 , then Find the value of a

A:

Q: The polynomial function B(x) = x' + 8x² + 5x = 14 has a known factor of (x + 2). Rewrite B(x) as a…

A: Here given (x+2) is a factor of function

Q: When we write the polynomial function that has 0,1,2 as the zeros, the resulting polynomial is -2x +…

A:

Q: Find a polynomial f(x) of degree 5 that has the following zeros. -4, -1, 6 (multiplicity 2), 0 Leave…

A:

Q: The polynomial function q(x) = 3x + 11x2 - 14x- 40 has a known factor of (3x+5). Rewrite g(x) as the…

A: Given, polynomial function qx=3x3+11x2−14x−40 and known factor 3x+5 To write: qx as the product of…

Q: E Given that x = 3 is a solution of f(x), factor f(x) =x'-10x² +33x-36 completely using long…

A:

Q: Use synthetic division to find the result when x + 2x2-11a + 24 is divided by x +5. If there is a…

A:

Q: The value of f(3) for the polynomial f(x)=x3+x2-5x+3 is 24. What does this mean in terms of…

A: Given:  f(x) = x3+x2-5x+3 Now we have f(3) = 24

Q: determine if the statement is true or false. If a statement is false, explain whyThe sum of two…

A: Given:The sum of two polynomials each of degree 5 will be less thanor equal to degree 5

Q: Find a, b, c e R such that the polynomial f(x) = x° + ax? + bx + c is divisible by g1(x) = x +2 and…

A: