Question

(1) 3x^3-2x-1 (2)x^3+6x^2+11x+6 (3)x^4+2x^3-9x^2-2x+8 (4) (x^2+3x+2)(x^2+7x+12)-120. 因式分解

Answer 1

(1) 3x^3-2x-1=(3x+1)(x-1)
(2)x^3+6x^2+11x+6
=x^3+2x^2+4x^2+8x+3x+6
=x^2(x+2)+4x(x+2)+3(x+2)
=(x+2)(x^2+4x+3)
=(x+2)(x+1)(x+3)
(3)x^4+2x^3-9x^2-2x+8
= x^4-2x^3+4x^3-8x^2-x^2+2x-4x+8
=x^3(x-2)+4x^2(x-2)-x(x-2)-4(x-2)
=(x-2)(x^3+4x^2-x-4)
=(x-2)(x+4)(x^2-1)
=(x-2)(x-4)(x+1)(x-1)
(4) (x^2+3x+2)(x^2+7x+12)-120
=(x+2)(x+1)(x+3)(x+4)-120
=(x+2)(x+3)(x+1)(x+4)-120
=(x^2+5x+6)(x^2+5x+4)-120
=(x^2+5x)^2+10(x^2+5x)+24-120
=(x^2+5x)^2+10(x^2+5x)-96
=(x^2+5x-6)(x^2+5x+16)
=(x+6)(x-1)(x^2+5x+16)