Question

Factor completely:

a) x^3-4x^2-11x+30


b) 2x^3+3x^2-1

Answer 1

use factor and remainder theorems..

Answer 2

x^3-4x^2-11x+30
=x^3-2x^22x^2+4x-15x+30
=x^2(x-2) -2x(x-2) -15(x-2)
=(x-2)(x^2-2x-15)
=(x-2)(x^2-5x+3x-15)
=(x-2)( x(x-5) +3(x-5))
=(x-2)(x+3)(x-5)

Answer 3

2x^3+3x^2-1
=2x^3+3x^2-3+2
=2(x^3+1) +3(x^2-1)
=2(x+1)(x^2-x+1)+3(x+1)(x-1)
=(x+1)(2x^2 -2x+2+3x-3)
=(x+1)(2x^2 -x -5)