Question

这几题因式分解怎么做啊？

Answer 1

x^3+x^2-10x-6
x^3+x^2-10x-6
= x^3+x^2-12x+2x-6
=x(x²+x-12)+2(x-3)
=x(x+4)(x-3)+2(x-3)
=(x-3)(x²+4x+2)

x^4+3x^3-3x^2-12x-4
=x^4+3x^3+2x^2-5x^2-12x-4
=x²(x²+3x+2)-(5x^2+12x+4)
=x²(x+2)(x+1)-(5x+2)(x+2)
=(x+2)[x²(x+1)-(5x+2)]
=(x+2)(x³+x²-5x+2)

4x^4+4x^3-9x^2-x+2
=4x^4+4x^3-8x^2-x^2-x+2
=(4x^4+4x^3-8x^2)-(x^2+x-2)
=4x^2(x^2+x-2)-(x^2+x-2)
=(4x^2-1)(x^2+x-2)
=(2x+1)(2x-1)(x-2)(x+1)