Question

因式分解 1.(y^2-1)(y+3)(y+5)-9 2.a^3+3a+50 3.(x^2+x+1)(x^2+x+2)-

Answer 1

1.

(y^2-1)(y+3)(y+5)-9

=(y-1)(y+1)(y+3)(y+5)-9

=(y-1)(y+5)(y+1)(y+3)-9

=(y^2+4y-5)(y^2+4y+3)-9

设y^2+4y=x,则

原式=(x-5)(x+3)-9=x^2-2x-15-9=x^2-2x-24=(x+4)(x-6)

则.

(y^2-1)(y+3)(y+5)-9

=(y^2+4y+4)(y^2+4y-6)

=(y+2)^2(y^2+4y-6)

2.题目有没有错?请再查一下,可追问

3.

(x^2+x+1)(x^2+x+2)-12

=(x²+x)²+3(x²+x)+2-12

=(x²+x)²+3(x²+x)-10

=(x²+x-2)(x²+x+5)

=(x-1)(x+2)(x²+x+5)

4.

5.(x^3+6x^2+11x+6)

=(x^3+3x^2)+(3x^2+11x+6)

=x^2(x+3)+(x+3)(3x+2)

=(x+3)(x^2+3x+2)

=(x+3)(x+2)(x+1)