Use the factor theorem to factorise completely x^3 + x^2 - 4x - 4… - Vidyadip

Question

Use the factor theorem to factorise completely $x^3 + x^2 - 4x - 4$.

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Answer

$\mathrm{x} 3+\mathrm{x} 2-4 \mathrm{x}-4$
$\text { Let } \mathrm{x}+1=0$
$\therefore \mathrm{x}=-1$
On substituting value of $x$ in the expression
$\therefore f(-1)=(-1)^3+(-1)^2-4(-1)-4=0$
Clearly $x+1$ is a factor of
$f(x)=x^3+x^2-4 x-4$
$\therefore f(x)=(x+1)\left(x^2-4\right) \ldots($ By actual division)
$=(x+1)(x-2)(x+2)$

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