Question

因式分解： x^3+6x^3+11x+6 6x^4+5x^3+3x^2-3x-2 x^4-11x^2+1 2x^3-ax^2-5a^2x-2a^3

x^3+6x^2+11x+6

6x^4+5x^3+3x^2-3x-2

x^4-11x^2+1

2x^3-ax^2-5a^2x-2a^3

Answer 1

1.X^3+6X^2+11X+6
=(X^3+X^2)+(5X^2+5X)+(6X+6)
=X^2(X+1)+5X(X+1)+6(X+1)
=(X+1)(X^2+5X+6)
=(X+1)(X+2)(X+3)

2. 6x^4+5x^3+3x^2-3x-2
=6x^4+5x^3+(x^2+2x^2)-3x-2
=(6x^4+5x^3+x^2)+(2x^2-3x-2)
=x^2(2x+1)(3x+1)+(2x+1)(x-2)
=(2x+1)(3x^3+x^2+x-2)
=(2x+1)(3x^3-3+x^2+x+1)
=(2x+1)[3(x-1)(x^2+x+1)+x^2+x+1]
=(2x+1)(3x-2)(x^2+x+1)

3.x^4-11x^2+1
=(x^4-2x^2+1)-9x^2
=(x^2-1)^2-(3x)^2
=(x^2+3x-1)(x^2-3x-1)

4.2x^3-ax^2-5a^2x-2a^3
=2x^3-ax^2-(2a^2x+3a^2x)-2a^3
=(2x^3-2a^2x)-(ax^2+3a^2x+2a^3)
=2x(x+a)(x-a)-a(x+a)(x+2a)
=(x+a)[2x(x-a)-a(x+2a)]
=(x+a)[2x^2-3ax-2a^2]
=(x+a)(x-2a)(2x+a)

Answer 2

6x^4+5x^3+3x^2-3x-2
=6x^4+(5x+4)x^2-(x^2+3x+2)
=6x^4+(5x+4)x^2-(x+1)(x+2)
=(x^2+x+1)(6x^2-x-2)
=(2x+1)(3x-2)(x^2+x+1)