Question

Which of the following is a factor of 5x3 − 135

A. 5
B. x + 3
C. x2 − 3x + 9
D. All of the above

Answer 1

5x³ - 135 =
5(x³-27) =
5(x³ - 3³) =
5(x-3)(x²+3x+9)

Answer: A.

Answer 2

Option A is correct

5 is a factor of
`5x^3-135`

Explanation:

To factor the
`5x^3-135`

we can write 135 as:

`135 =5 \cdot 3^3`

then;

`5x^3-5 \cdot 3^3`

Take 5 common we have;

`5(x^3-3^3)`

using identity rule:

`(x^3-a^3) = (x-a)(x^2+ax+a^2)`

\then;

`5 \cdot (x-3) \cdot (x^2-3x+9)`

⇒the factor of
`5x^3-135` are: 5, x-3 and
`x^2-3x+9`

Therefore, from the given options the following factor of
`5x^3-135` is, only 5