Mathematics: 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).

When factored completely, x 3 − 9 x is equivalent

jordantay208

20.01.2022

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.

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