Question

factor the following expression.
$28u^{2}v^{5}x^{4} + 12u^{5}v^{9}$

Explanation:

Step1: Find GCF of coefficients

The coefficients are 28 and 12. Prime factors: \(28 = 2^2\times7\), \(12 = 2^2\times3\). GCF is \(2^2 = 4\).

Step2: Find GCF of variables

For \(u\): lowest power is \(u^2\). For \(v\): lowest power is \(v^5\). For \(x\): only in first term, so no \(x\) in GCF.

Step3: Factor out GCF

\(28u^2v^5x^4 + 12u^5v^9 = 4u^2v^5(7x^4 + 3u^3v^4)\)

Answer:

\(4u^2v^5(7x^4 + 3u^3v^4)\)