因式分解,万分火急!x^2+(a+1)x-(6a^2-13a+6)x^4+x^3+4x^2+3x+3x^5-x^4+x^3-x^2+x-1(a+2b+c)^3-(a+b)^3-(b+c)^3

Question

因式分解,万分火急!
 x^2+(a+1)x-(6a^2-13a+6)
x^4+x^3+4x^2+3x+3
x^5-x^4+x^3-x^2+x-1
(a+2b+c)^3-(a+b)^3-(b+c)^3

Answer 1

x²+(a+1)x-(6a²-13a+6)
=x²+(a+1)x-(3a-2)(2a-3)
=[x+(3a-2)][x-(2a-3)]
=(x+3a-2)(x-2a+3)
x^4+x³+4x²+3x+3
=x^4+x³+x²+3x²+3x+3
=x²(x²+x+1)+3(x²+x+1)
=(x²+x+1)(x²+3)
x^5-x^4+x³-x²+x-1
=x^4(x-1)+x²(x-1)+(x-1)
=(x-1)(x^4+x²+1)
(a+2b+c)³-(a+b)³-(b+c)³
=[(a+b)+(b+c)]³-(a+b)³-(b+c)³
=(a+b)³+3(a+b)²(b+c)+3(a+b)(b+c)²+(b+c)³-(a+b)³-(b+c)³
=3(a+b)²(b+c)+3(a+b)(b+c)²
=3(a+b)(b+c)(a+b+b+c)
=3(a+b)(b+c)(a+2b+c)