帮做几道因式分解题1x^5+x-12a^2-b^2+4a+2b+33x^2-(p^2+q^2)x+pq(p+q)(p-q)4x^6+64y^6+12x^2y^2-152a^2b^2+2b^2c^2+2c^2a^2-a^4-b^4-c^46x^4+4x^3+10x^2+12x+9

Question

帮做几道因式分解题
1 x^5+x-1
2 a^2-b^2+4a+2b+3
3 x^2-(p^2+q^2)x+pq(p+q)(p-q)
4 x^6+64y^6+12x^2y^2-1
5 2a^2b^2+2b^2c^2+2c^2a^2-a^4-b^4-c^4
6 x^4+4x^3+10x^2+12x+9

Answer 1

1.x^5+x-1 = x^5+x^2-x^2+x-1 = x^2(x^3+1)-(x^2-x+1) = (x^3+x^2-1)(x^2-x+1)
2.a^2-b^2+4a+2b+3 = (a+2)^2-(b-1)^2 =(a+2+b-1)(a+2-b+1)=(a+b+1)(a-b+3)
3.双十字相乘法

x````````````-p(p-q)
x````````````-q(p+q)
交叉相乘再 相加即为一次项系数
[x-q(p+q)][x-p(p-q)]
4.5.让下班了今天晚上研究一下.明天告诉你
6.x^4+4x^3+10x^2+12x+9=(x^4+2x^3+3x^2)+(2x^3+4x^2+6x)+(3x^2+6x+9)=(x^2+2x+3)(x^2+2x+3)=(x^2+2x+3)^2