Question

7• f(x) = 2x³ - 32x

Explanation:

Assuming the problem is to factor the function \( f(x) = 2x^3 - 32x \):

Step 1: Factor out the greatest common factor (GCF)

The GCF of \( 2x^3 \) and \( -32x \) is \( 2x \). So we factor that out:
\( f(x) = 2x(x^2 - 16) \)

Step 2: Factor the difference of squares

The expression \( x^2 - 16 \) is a difference of squares, which can be factored as \( (x - 4)(x + 4) \) (since \( a^2 - b^2=(a - b)(a + b) \) with \( a = x \) and \( b = 4 \)):
\( f(x)=2x(x - 4)(x + 4) \)

Answer:

\( f(x)=2x(x - 4)(x + 4) \)