2x^5+7x^4+12x^3+14x^2+10x+3因式分解

2x^5+7x⁴+12x³+14x²+10x+3
=2x^5+2x⁴+5x^4+5x³+7x³+7x²+7x²+7x+3x+3
=2x⁴(x+1)+5x³(x+1)+7x²(x+1)+7x(x+1)+3(x+1)
=(x+1)(2x⁴+5x³+7x²+7x+3)
=(x+1)(2x⁴+2x³+3x³+3x²+4x²+4x+3x+3)
=(x+1)[2x³(x+1)+3x²(x+1)+4x(x+1)+3(x+1)]
=(x+1)²(2x³+3x²+4x+3)
=(x+1)²(2x³+2x²+x²+x+3x+3)
=(x+1)²[2x²(x+1)+x(x+1)+3(x+1)]
=(x+1)³(2x³+x+3)