# 2.(ii) Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:   (ii)    $p(x) = x^3 + 3x^2 + 3x + 1, \ g(x) = x + 2$

G Gautam harsolia

Zero of polynomial  $g(x)=x+2$  is  $-2$

If  $g(x)=x+2$  is factor of polynomial  $p(x) = x^3 + 3x^2 + 3x + 1$

Then,  $p(-2)$  must be equal to zero

Now,

$\Rightarrow p(-2) = (-2)^3 + 3(-2)^2 + 3(-2) + 1$

$\Rightarrow p(-2)= -8+12-6+1 = -1\neq 0$

Therefore,  $g(x)=x+2$   is not a factor of polynomial  $p(x) = x^3 + 3x^2 + 3x + 1$

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