Question

Factorize : 2x 3 - x 2 -13x - 6

Answer 1

p(x)= 2x3-x2-13x-6
P(-2)=2(-2)^3-(-2)^2-13(-2)-6
=-16-4+26-6
=-26+26
=0
THEREFORE
x+2 is a factor of p(x)
p(x)=(x+2)(2x^2-5x-3)

=(x+2)(2x^2-6x+x-3)
=(x+2)(2x+1)(x-3)

Answer 2

$\bold{x=-2,-\frac{1}{2} \text { and } 3}$is the value of  x  for the given cubic polynomial $\bold{2 x^{3}-x^{2}-13 x-6}$

Given:

$2 x^{3}-x^{2}-13 x-6$

To find:

The value of x

Solution:

From the given $2 x^{3}-x^{2}-13 x-6$  to find the value of x solve the cubic polynomial and convert them in to quadratic equation and then find the roots.

First to solve cubic polynomial use synthetic division then the result is the quadratic equation.

$(x+2)\left(2 x^{2}-5 x-3\right)=0$

Then solving the quadratic equation using the formula $\bold{\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}}$

The quadratic equation is $2 x^{2}-5 x-3$

$\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ where a=2,b=-5 and c=-3

$\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}=\frac{5 \pm \sqrt{25-4(2)(-3)}}{2(2)}=\frac{5 \pm 7}{4}=\frac{12}{4},-\frac{2}{4}=3,-\frac{1}{2}$

The value of$\bold{x=-2,3,-\frac{1}{2}}$ for the cubic polynomial  $\bold{2 x^{3}-x^{2}-13 x-6.}$