Question

Factorise the polynomial $2y^3+y^3-2y-1$

• A. $(y+1)(y+1)(2y+1)$
• B. $(y-1)(y-1)(2y+1)$
• C. $(y-1)(y+1)(2y+1)$
• D. $(y-1)(y-1)(2y-1)$

Answer 1

The correct option is C $(y-1)(y+1)(2y+1)$

Let $p\left(y\right)=2y^3+y^3-2y-1$
By trail, we find that $p\left(1\right)=2(1{)}^3+(1{)}^2-2\left(1\right)-1=2+1-2-1=0$
$\Rightarrow (y-1)$ is a factor of the polynomial p(y).
Now, $2y^3+y^3-2y-1$
$=(2y^3-2y^2)+(3y^2-3y)+(y-1)$
$=2y^2(y-1)+3y(y-1)+1(y-1)$
$=(y-1)(2y^2+3y+1)$
$=(y-1)\{2y^2+2y+y+1\}$
$=(y-1)\left\{2y\right(y+1)+1(y+1\left)\right\}$
$=(y-1)\left\{\right(y+1\left)\right(2y+1\left)\right\}$
$=(y-1)(y+1)(2y+1)$