How do you factor x4 + 6×3 – 36×2 – 216x

# How do you factor x4 + 6x3 – 36x2 – 216x

1. A
(x + 1) (x + 2)
2. B
x (x + 2) (x + 1)
3. C
x (x + 1) (x + 2)
4. D
x (x – 1) (x + 6)2

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### Solution:

We take x = 0
6x (– 216)
= –1296
So, (x = 0) is not a root of equation
When x = 6
6(16)3 + 6(6)3 – 36(6) –216)
6(216 + 216 – 216 – 216)
6 × 0 = 0
So, x = 6 is a factor so
x (x2 (x – 6) + 12x (x – 6) + 36 (x –6))
= x (x – 6) (x2 +12 x + 36)
x (x – 6) (x2 + 6x + 36)
= x (x – 6) (x (x + 6) + 6 (x + 6))
= x (x – 6) (x +6)2 is

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