Question

Using factor theorem, factorise the polynomial x4 - 2x3 - 7x2 + 8x + 12.​

Answer 1

Answer:

${\huge{\underline{\underline{\bold{\red{\:\:\:Answer:-\:\:\:}}}}}}$

$x^4-2x^3-7x^2+8x+12$

$=x^4-3x^3+x^3-3x^2-4x^2+12x-4x+12$

$=x^3 (x-3)+x^2 (x-3)-4x (x-3)-4 (x-3)$

$=(x-3)(x^3+x^2-4x-4)$

$=(x-3)(x^3+2x^2-x^2-2x-2x-4)$

$=(x-3)[x^2 (x+2)-x (x+2)-2 (x+2)]$

$=(x-3)(x+2)(x^2-x-2)$

$=(x-3)(x+2)(x^2+x-2x-2)$

$=(x-3)(x+2)[x (x+1)-2 (x+1)]$

$=(x-3)(x+2)(x+1)(x-2)$