If the remainder is zero (0) when f(x) is divided by x-4, this means that x-4 is a ____

Q: Determine the value of k such that when f(x)=x* - kx +7x-6 is divided by x - 2, the remainder is 4.

A: We have to find the value of k. To solve this problem we will use 'Remainder theorem' which states…

Q: If f is a polynomial function and x-4 is a factor of f, then f (4) .

A: A polynomial function is a function that involves only positive powers in equation . The general…

Q: If f(-6) = 6 and f '(x) < 8 for all x, what is the largest possible value of f (3)?

A:

Q: In Problem,use the Intermediate Value Theorem to show that each polynomial function has a zero in…

A: The intermediate Value Theorem states that if any function f(x) is continuous in the given interval…

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

A:

Q: Find all rational zeros of: f(x) = 2x^4 − 11x^3 + 14x^2 − 11x + 12

A: The rational zeros of a polynomial fx=anxn+an-1xn-1+...+a0 are numbers of the type pq , q≠0 Here, p…

Q: 15. Determine the zeros for and the end behavior of f(x) = x(x – 4)(x +2)*.

A: Given function is  F(x) = x(x-4)(x+2)^2

Q: For f(x)=-5x+3 and g(x)=square root x-5 Find f^-1(x)

A: Given

Q: Find k so that f(x)=2x² +12x + k has one root.

A:

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: List all possible rational zeros for the function f(x) = x4 + 8x3 − 9x + 9.

A:

Q: The polynomial function f ( x ) = x 3 − 3 x 2 + 25 x − 75 has 5 i as a zero. What is the only real…

A:

Q: Find the other zeros of f (x) = 3x* – 16x + 14x² + 24x – 9, if 3 is a zero of a function.

A: We will solve it by division algorithm Given f(x) = 3x4-16x3+14x2+24x-9 Given 3 is the zero of the…

Q: What effect does the “k” in f(x)= ^3 √x+k have on The graph of the cube root function ^3 √x and…

A: Given the function We have to find the effect of the k in the above function.

Q: Given that f(x)=x^2+3x-70f(x)=x2+3x−70 and g(x)=x-7g(x)=x−7, find (f-g)(x)(f−g)(x) and express the…

A: Given,

Q: 11. Find the domain of √√x-4 x² - 6x f(x)=

A:

Q: 4. For the function f(x) x+ 8x + 5x2-38x + 24, use long division to determine whether each of the…

A:

Q: 1. How many non-real zeros does the function f(x) = x - 2x + 8x-16x have? 1. 0 2. 2 3. 3 4. 4

A:

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

A: Given

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: 21. Find the "natural" domain of the function f(x)= 4x-10x+4

A:

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: Find the asymptotes of the functions: 4x2 1- f(x) = x² +8 x2-6x+7 2- f(x) x+5

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Q: A polynomial f(x) and one or more of its zeros are given. f(x)=x²-2x³+3x²+4x-10 1-2i is a zero

A:

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

A:

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: 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: The graph of f (x)3-x²-5x+6 has the point (2, -6) on it. O True O False

A: Given statement  The graph of f(x)=-x^2-5x+6 has the point (2,-6) on it

Q: Given that f(x) =x^2 -2 and g(x)=6x+3 find (f-g) (-2) if it exists

A: Consider the given equations

Q: Given f(x)= -9x^7 - x^6 +4x^3 - 3 and g(x) = -9x^7 - 5x^3 - 9x^2 + 2, find and simplify f(x) - g(x).…

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Q: 1) Which set of values for x should be tested to determine the possible zeros of the function f (x)…

A: We need to find possible x values that needs to be checked where function is zero.   NOTE - As per…

Q: 3. Find all the zeros for: f(x) = x3 - 2x2 - 5x + 6

A: Given that, y = x3 - 2x2 -5x + 6 and we have to calculate the zeros of the function. We know that,…

Q: 27. Factor f(x) = 15x – 67x + 26x + 8, given that is a zero of f(x).

A:

Q: The function f(x) = kx3 – 8x2 –x +3k +1 has a zero when x= 2. Determine the value of k and all the…

A: We will first use the condition that x=2 is a zero of f(x) to get value of k then we will use…

Q: If f is a polynomial function and x−5 is a factor of​ f, then ​f(5)=

A:

Q: If f is a polynomial function and x-5 is a factor of f, then f(5) =

A:

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

A:

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

A: Given function

Q: Which of the following are vertical asymptotes of f(x) = x2 - 2X 7 x² – 4 x=0 x=-1 x=-2 X=1 x=2

A: Recall:  To find vertical asymptote, set the denominator equal to zero and solve for x. Given,…

Q: Find the possible rational zeros of the functions: f(x) =-x +3x² +4 g(x)= 2x +6x-11x+8

A: Given:       fx=-x4+3x2+4 Since all coefficients are integers, we can apply the rational zeros…

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

A:

Q: Find the asymptotes of the functions: 4x2 1- f(x) = x² +8

A: As per our guidelines we need to solve only one question.Please repost the other remaining question…

Q: Suppose​ f(x) is a 7th degree polynomial. Using a few complete​ sentences, explain why we are…

A: Given f(x) is a 7th degree polynomial.  Recall: fundamental theorem of algebra:  If f(x) is a…

Q: If f(-9) = 2 andf'(x) < 9 for all x, what is the largest possible value of f(1)?

A: Lagrange's Mean Value Theorem : If f(x) be continuous on [a, b] and differentiable on (a, b) then…

Q: Find all zeros of the following: f(x)=x3+2x2- 10x+4 f(x)=4x3-7x2-20x+35 f(x)=x3-9x2+31x-39 f(x)=…

A: Consider the given polynomial function

Q: find all the rational zeros of the function. f(x)=4x^3-27x^2+11x+42 f(x)=x^4+x^3-11x^2+x-12

A:

Q: 9. Find all real zeroes of the function p(x)=6x' +17x² – 26x +8

A: Definition used-              Rational zero theorem  -                       If a…

Q: One factor of f(x) = x³ – 7x2 - 20x + 96 is x - 3. What are the zeros of f(x)? (Enter your answers…

A: Given:The given function is f(x)=x3-7x2-20x+96and one factor is given i.e. (x-3) To…

Q: Find all zeros of f (x) = x - 3x3+ 6x2 + 2x- 60 given that 1 +3i is a zero of f (x).

A: Complex roots always exist in conjugate pair. Use this concept for finding other zeros.

Q: If f (x) = x- x² 17x 15 and a +1 is a factor of f (x), then find all of the zefos of f(x)…

A: Solution: The objective is to find the zeros of the given polynomial