Factor x 3 – 6 x 2 + 5 x + 12?

${\mathrm{Factor\; x}}^{}$${}^{}$$–$$6$$x^{}$${}^{}$$+$$5$$x$$+$$\mathrm{12?}$

 

Ans:-

$\Rightarrow (x+1)(x-3)(x-4)$

Factors are $x=-1,3,4$

Explanation:

$(x^3-6x^2+5x+12)$

Since the sum of the coefficients of the terms is zero, $x+1$ is a factor.

Using synthetic division,

$aaa-1aaa\mid aaa1aaa-6aaa5aaa12$

$aaaaaaaaa\mid aaa\downarrow aa-1aaa7a-12$

$aaaaaaaaa\mid \dots \dots \dots \dots \dots \dots \dots \dots \dots$

$aaaaaaaaaaaaaa1aaa-7aaa12aaa0$

$\Rightarrow (x+1)(x^2-7x+12)$

$\Rightarrow (x+1)(x^2-3x-4x+12)$

$\Rightarrow (x+1)(x(x-3)-4(x-3))$

$\Rightarrow (x+1)(x-3)(x-4)$

Factors are $x=-1,3,4$