6x^4+5x^3+25x^2+20x+4如何化简为：(x+1/2)(x+1/3)(6x^2+24)

Question

6x^4+5x^3 +25x^2 +20x +4 如何化简为：(x+1/2)(x+1/3)(6x^2+24)

Answer 1

其实这个答案：(x+1/2)(x+1/3)(6x^2+24)还可以化简的.,最后一个式子可以提取公约数6
6x^4+5x^3 +25x^2 +20x +4=6x^4+24x^2 +5x^3+x^2+20x +4 (提取公因式)
=6x^2（x^2+4）+x^2(5x+1)+4(5x+1)
=6x^2（x^2+4）+(5x+1)(x^2+4)
=（x^2+4）(6x^2+5x+1) （十字相乘）
=（x^2+4）(2x+1)(3x+1) (分别乘以6,1/2,1/3,等式不变)
=（6x^2+24）(x+1/2)(x+1/3)