Question

因式分解:x^4+2x^3-9x^2-2x+8

Answer 1

=x^4+x³+x³+x²-10x²-10x+8x+8
=x³(x+1)+x²(x+1)-10x(x+1)+8(x+1)
=(x+1)(x³+x²-10x+8)
=(x+1)(x³-x²+2x²-2x-8x+8)
=(x+1)(x-1)(x²+2x-8)
=(x+1)(x-1)(x+4)(x-2)

Answer 2

x^4+2x³-9x²-2x+8
=x^4-2x³+4x³-8x²-x²+2x-4x+8
=x³(x-2)+4x²(x-2)-x(x-2)-4(x-2)
=(x-2)(x³+4x²-x-4)
=(x-2)[x²(x+4)-(x+4)]
=(x-2)(x+4)(x²-1)
=(x-2)(x+4)(x+1)(x-1)

Answer 3

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

Answer 4

=x^4 - x^3 + 3x^3 - 3x^2 - 6x^2 + 6x - 8x + 8
=(x-1)(x^3 +3x^2 - 6x - 8)
= (x-1)(x^3 + x^2 + 2x^2 + 2x - 8x - 8)
= (x-1)(x+1)(x^2 + 2x - 8)
= (x-1)(x+1)(x+4)(x-2)

Answer 5

=x^4+x³+x³+x²-10x²-10x+8x+8
=x³(x+1)+x²(x+1)-10x(x+1)+8(x+1)
=(x+1)(x³-x²+2x²-2x-8x+8)
=(x+1)(x-1)(x²+2x-8)
=(x+1)(x-1)(x+4)(x-2)