Question

question
factor completely:
$6g^4 + 2g^3 - 8g^2$

Explanation:

Step1: Find the GCF

The greatest common factor (GCF) of \(6g^4\), \(2g^3\), and \(-8g^2\) is \(2g^2\). Factor out \(2g^2\):
\(6g^4 + 2g^3 - 8g^2 = 2g^2(3g^2 + g - 4)\)

Step2: Factor the quadratic

Factor \(3g^2 + g - 4\). Find two numbers that multiply to \(3 \times (-4) = -12\) and add to \(1\). The numbers are \(4\) and \(-3\).
Rewrite the middle term: \(3g^2 + 4g - 3g - 4\)
Group and factor:
\(g(3g + 4) - 1(3g + 4) = (3g + 4)(g - 1)\)

Step3: Combine factors

Put it all together: \(2g^2(3g + 4)(g - 1)\)

Answer:

\(2g^2(3g + 4)(g - 1)\)