Use Factor Theorem to determine whether g(x) is a factor of p(x) in each of following cases : p(x)=x

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2. Polynomials

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Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=x^{3}+3 x^{2}+3 x+1$, $g(x)=x+2$.

Option A

Option B

Option C

Option D

Solution

We have $p ( x )= x ^{3}+3 x ^{2}+3 x +1$ and $g ( x )= x +2$

$p (-2)=(-2)^{3}+3(-2)^{2}+3(-2)+1$

$=-8+3(4)+(-6)+1=-8+12-6+1$

$=-8-6+12+1=-14+13=-1$

$\therefore $ $p(-2) \neq 0$

Thus, $g(x)$ is not a factor of $p(x)$.

Standard 9

Mathematics

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