Question

select the correct answer from each drop - down menu.
what is the factored form of this expression?
$8x^3 - 8x^2 - 30x = \square\\ (\square)(\square)$
reset next

Explanation:

Step1: Factor out GCF

First, find the greatest common factor (GCF) of \(8x^3\), \(-8x^2\), and \(-30x\). The GCF of the coefficients \(8\), \(-8\), \(-30\) is \(2\), and the GCF of the variable terms \(x^3\), \(x^2\), \(x\) is \(x\). So the GCF is \(2x\). Factor out \(2x\) from the expression:
\(8x^3 - 8x^2 - 30x = 2x(4x^2 - 4x - 15)\)

Step2: Factor the quadratic

Now factor the quadratic \(4x^2 - 4x - 15\). We need two numbers that multiply to \(4 \times (-15) = -60\) and add to \(-4\). The numbers are \(-10\) and \(6\). Rewrite the middle term:
\(4x^2 - 10x + 6x - 15\)

Group the terms:
\((4x^2 - 10x) + (6x - 15)\)

Factor out the GCF from each group:
\(2x(2x - 5) + 3(2x - 5)\)

Now factor out \((2x - 5)\):
\((2x - 5)(2x + 3)\)

Step3: Combine results

Putting it all together, the factored form is:
\(8x^3 - 8x^2 - 30x = 2x(2x - 5)(2x + 3)\)

Answer:

\(2x\), \(2x - 5\), \(2x + 3\) (in the respective boxes)