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webwork / hs rowe cpma / 6.1 greatest common factor / 10
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6.1 greatest common factor: f
(1 point)
factor out the greatest common factor:
$12 a^{2} b^{4}+9 a b-24 a=\square$
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Explanation:

Step1: Find the GCF of coefficients

Find the GCF of \(12\), \(9\), and \(24\).
Factors of \(12\): \(1,2,3,4,6,12\)
Factors of \(9\): \(1,3,9\)
Factors of \(24\): \(1,2,3,4,6,8,12,24\)
GCF of \(12\), \(9\), \(24\) is \(3\).

Step2: Find the GCF of variables

For variable \(a\):
Terms have \(a^{2}\), \(a\), \(a\). The lowest power of \(a\) is \(a\).
For variable \(b\):
Terms have \(b^{4}\), \(b\), no \(b\) (in the third term). So we don't include \(b\) in the GCF (since the third term has no \(b\) factor).
So the GCF of the polynomial \(12a^{2}b^{4}+9ab - 24a\) is \(3a\).

Step3: Factor out the GCF

Divide each term by \(3a\):
\(\frac{12a^{2}b^{4}}{3a}=4ab^{4}\), \(\frac{9ab}{3a} = 3b\), \(\frac{-24a}{3a}=-8\)

So \(12a^{2}b^{4}+9ab - 24a=3a(4ab^{4}+3b - 8)\)

Answer:

\(3a(4ab^{4}+3b - 8)\)