Question

factorize using factor theorem x^3 + x^2 - 4x -4

Answer 1

$\huge{\boxed{\red{\bf{Solution:-}}}}$

Let ${f(x)} = {x}^{3} + {x}^{2} - {4x} - {4}$

then,

let ${x} = {-1}$

${f(-1)} = {-1}^{3} + {-1}^{2} - {4×(-1)} - {4}$

${f(-1)} = {-1} + {1} + {4} - {4}$

${f(-1)} = {5} - {5}$

${f(-1)} = {0}$

(x+1) is a factor of f(x).

Dividing f(x) from (x+1), we get:-

${x}^{2} - {4}={0}$

Factorizing ${x}^{2} - {4}={0}$:-

${x}^{2} - {2}^{2}={0}$

${(x + 2)}{(x - 2)}={0}$

$\huge{\boxed{\red{\bf{Answer:-}}}}$

Hence the factors of f(x) are:-

(x - 2)(x + 1)(x + 2)