Question

When factored completely, x 3 − 9 x is equivalent to —

A. x( x + 3)( x − 3).
B. x( x + 3).
C. ( x + 3)( x − 3).
D. x( x − 3).

Answer 1

`x^3-9x` is equivalent to the expression x(x + 3)(x – 3).

Solution:

Given expression:

`x^3-9x`

To find the equivalent expression for the given expression.

`x^3-9x`

Take the common term x outside.

`x^3-9x=x(x^2-9)`

9 can be written as 3 × 3 = 3²

`=x(x^2-3^2)`

Using the algebraic identity:
`a^2-b^2=(a+b)(a-b)`

`=x(x+3)(x-3)`

`x^3-9x=x(x+3)(x-3)`

Hence
`x^3-9x` is equivalent to the expression x(x + 3)(x – 3).

Option A is the correct answer.