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HELP PLEASEE EASY QUESTION


Which statements are true about the polynomial function?

f(x)=x3−x2−4x+4

Select each correct answer.




f(x)=0 when x=−1 .

f(−1)=0

(x−1) is a factor of f(x) .

f(x) divided by (x−1) has a remainder of 0.

Respuesta :

Answer:

D. f(x)  divided by (x−1)  has a remainder of 0.

C. (x−1)  is a factor of  f(x) .

Step-by-step explanation:

Just took a test with this question these are the answers!

abidemiokin

The statements that are true about the polynomial function are;

  • (x−1) is a factor of f(x).  
  • f(x) divided by (x−1) has a remainder of 0.

Given the polynomial function [tex]f(x)=x^3-x^2-4x+4[/tex]

If x = -1, hence;

[tex]f(-1)=(-1)^3-(-1)^2-4(-1)+4\\f(-1)=-1-1+4+4\\f(-1)=-2+8\\f(-1) =6[/tex]

This shows that f(x) ≠ 0 when x = −1 .

To check if x - 1 is a factor, we will substitute x = 1 into the function and check if the result is zero as shown:

[tex]f(1)=1^3-1^2-4(1)+4\\f(1)=1-1-4+4\\f(1) =0[/tex]

  • This shows that (x−1) is a factor of f(x).

  • This also shows that if f(x) divided by (x−1) has a remainder of 0.

Learn more here: https://brainly.com/question/18820029

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