一些因式分解题①x³+4x²-9;②x³+5x²-18;③x³+6x²+11x+6;④x³-11x²+31x-21.

Question

一些因式分解题
①x³+4x²-9; ②x³+5x²-18; ③x³+6x²+11x+6; ④x³-11x²+31x-21.

Answer 1

①x³+4x²-9;
=x³+3x²+x²-9
=x²(x+3)+(x+3)(x-3)
=(x+3)(x²+x-3)

②x³+5x²-18;
=x³+3x²+2x²-18
=x²(x+3)+2(x+3)(x-3)
=(x+3)(x²+2x-6)

③x³+6x²+11x+6;
=x³+6x²+9x+2x+6
=x(x+3)²+2(x+3)
=(x+3)(x²+3x+2)
=(x+3)(x+2)(x+1)

④x³-11x²+31x-21.
=x³-x²-10x²+10x+21x-21
=x²(x-1)-10x(x-1)+21(x-1)
=(x-1)(x²-10x+21)
=(x-1)(x-3)(x-7)