Question

Factorize the given equation $2y^3+y^2-2y-1$.

Answer 1

Factorize$\mathbf{2}{\mathit{y}}^{\mathbf{3}}\mathbf{+}{\mathit{y}}^{\mathbf{2}}\mathbf{-}\mathbf{2}\mathit{y}\mathbf{-}\mathbf{1}$.

First, take out the common terms.

$2y^3+y^2-2y-1=y^2(2y+1)-1(2y+1)$

$=(2y+1)(y^2–1)$

$=(2y+1)(y^2–1^2)$

$=\left(2y+1\right)\left(\left(y+1\right)\left(y-1\right)\right)$ $\left[\therefore a^2-b^2=\left(a+b\right)\left(a-b\right)\right]$

$=\left(2y+1\right)\left(y+1\right)\left(y-1\right)$

Hence the factored expression is$\left(2y+1\right)\left(y+1\right)\left(y-1\right)$.