Question

因式分解2x五次方-5x四次方-11x三次方+23x平方+9x-18

Answer 1

2x^5-5x^4-11x^3+23x^2+9x-18
=2x^5-2x^4-3x^4+3x^3-14x^3+14x^2+9x^2-9x+18x-18
=2x^4(x-1)-3x^3(x-1)-14x^2(x-1)+9x(x-1)+18(x-1)
=(2x^4-3x^3-14x^2+9x+18)(x-1)
=(2x^4-6x^3+3x^3-9x^2-5x^2+15x-6x+18)(x-1)
=[2x^3(x-3)+3x^2(x-3)-5x(x-3)-6(x-3)](x-1)
=(2x^3+3x^2-5x-6)(x-3)(x-1)
=(2x^3+2x^2+x^2+x-6x-6)(x-3)(x-1)
=(2x^2+x-6)(x+1)(x-3)(x-1)
=(2x-3)(x+2)(x+1)(x-3)(x-1)