Question

因式分解

a的立方+3*a的平方+50
a的立方+5a-5*a的平方-4
x的立方+x+30
在线等 答完给分

Answer 1

1.用试根法,a = -5 是方程a^3 + 3a^2 + 50 = 0 的一个根,所以a^3 + 3a^2 + 50 有一个因式为 (a + 5),有多相式除法得:

a^3 + 3a^2 + 50 = (a + 5)(a^2 - 2a + 10)

2. a^3 - 5a^2 + 5a - 4 = a^3 - 5a^2 - (a^2 - 5a + 4)

= a^2(a - 4) - (a - 4)(a - 1)

=(a - 1)(a^2 - a +1)

3.x^3 + x + 30 = x^3 +3x^2 -(3x^2 - x - 30)

= x^2(x + 3) - ((x+3)(3x -10)

= (x + 3)(x^2 - 3x + 10)