Question

Factorise: $2x^3-3x^2-17x+30$

Answer 1

Factorization

The given equation is,

$2x^3-3x^2-17x+30=2x^3+2x^2-12x-5x^2-5x+30$

$=2x(x^2+x-6)-5(x^2+x-6)$

$=(x^2+x-6)(2x-5)$

$=(x^2+3x-2x-6)(2x-5)$

$=\left\{x\right(x+3)-2(x+3\left)\right\}(2x-5)$

$=(x+3)(x-2)(2x-5)$

Hence, the result of the factorization of the given expression is $(x+3)(x-2)(2x-5)$.