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Is the binomial a factor of the polynomial function?f (x) = x^3 + 4x^2 - 9x - 36

Is The Binomial A Factor Of The Polynomial Functionf X X3 4x2 9x 36 class=

Sagot :

In order to find if each binomial is a factor of the given polynomial function, we can use the zero remainder theorem.

This theorem states that if a value x = k is a zero of the function f(x) (that is, f(k) = 0), so the binomial (x - k) is a factor of the function f(x).

Therefore, let's check the values 1, 3, -3, 4 and -4:

[tex]\begin{gathered} f(1)=1+4-9-36=-40 \\ f(3)=27+36-27-36=0 \\ f(-3)=-27+36+27-36=0 \\ f(4)=64+64-36-36=64 \\ f(-4)=-64+64+36-36=0 \end{gathered}[/tex]

Therefore the answer is:

(x - 1): No

(x - 3): Yes

(x + 3): Yes

(x - 4): No

(x + 4): Yes

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