分类：教育/科学-理工学科-数学
问题：因式分解x^4+3x^3
x^4+3x^3-3x^2-11x-68x^4+6x^3-19x^2+3x+22x^5+7x+12x^3+x^2+10x+3
回答：1、x⁴+3x³-3x²-11x-6=x⁴+3x³+2x²-5x²-11x-6=x²（x²+3x+2)-(5x²+11x+6)=x²（x+1)(x+2)-(5x+6)(x+1)=(x+1)(x³+2x²-5x-6)=(x+1)(x³+2x²+x-6x-6)=(x+1)[x（x²+2x+1)-(6x+6)]=(x+1)[x(x+1)²-6（x+1)]=(x+1)²（x²+x-6)=(x+1)²（x-2)(x+3)2、8x⁴+6x³-19x²+3x+2=8x⁴+6x³-20x²+x²+3x+2=2x²（4x²+3x-10）+（x²+3x+2）=2x²（4x-5)(x+2)+(x+1)(x+2)=(x+2)（8x³-10x²+x+1)=(x+2)（8x³-10x²+2x-x+1)=(x+2)[2x（4x²-5x+1)-(x-1)]=(x+2)[2x(4x-1)(x-1)-(x-1)]=(x+2)(x-1)(8x²-2x-1)=(x+2)(x-1)(4x+1)(2x-1)3、2x^5+7x⁴+12x³+x²+10x+3=2x^5+2x⁴+5x⁴+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)