Question

Factorise the expression 2x^3 + 9x^2 + 7x - 6 using the Factor Theorem.

Answer 1

Hi,

Explanation:

`P(x)=2x^3+9x^2+7x-6\\P(-2)=2*(-2)^3+9*(-2)^2+7*(-2)-6=-16+36-14-6=0\\P(-3)=2*(-3)^3+9*(-3)^2+7*(-3)-6=-54+81-21-6=0`

`\begin{array}cccc&x^3&x^2&x&1\\---&---&---&---&---\\&2&9&7&-6\\x=-2&&-4&-10&6\\&2&5&-3&0\\x=-3&&-6&3&\\&2&-1&0&\\\end {array}\\\\P(x)=(x+2)(x+3)(2x-1)\\`

An other way is:

`2x^3+9x^2+7x-6\\=2x^3+4x^2+5x^2+10x-3x-6\\=2x^2(x+2)+5x(x+2)-3(x+2)\\=(x+2)(2x^2+5x-3)\\=(x+2)(2x^2+6x-x-3)\\=(x+2)(2x(x+3)-(x+3))\\\\=(x+2)(x+3)(2x-1)\\`