用拆项法完成下列3道题目（1）x3次＋x2次-2（2）x3次-7x+6(3)x4次+x2次+1

Question

用拆项法完成下列3道题目
（1）x3次＋x2次-2 （2）x3次-7x+6 (3) x4次+x2次+1

Answer 1

=x^3-1+x^2-1

=(x-1)(x^2+x+1)+(x-1)(x+1)
=(x-1)(x^2+2x+2)

=x^3-1-7x+7
=(x-1)(x^2+x+1)-7(x-1)
=(x-1)(x^2+x-6)
=(x-1)(x+3)(x-2)

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