Question

the expression completely. $8x^{3}+5x$

Explanation:

Step1: Identify the GCF

The terms are \(8x^{3}\) and \(5x\). The greatest common factor (GCF) of the coefficients 8 and 5 is 1 (since 5 is prime and doesn't divide 8). For the variable part, the lowest power of \(x\) is \(x\) (from \(5x\)). So the GCF is \(x\).

Step2: Factor out the GCF

Factor out \(x\) from \(8x^{3}+5x\):
\(8x^{3}+5x = x(8x^{2}+5)\)
We check if \(8x^{2}+5\) can be factored further. Since \(8x^{2}+5\) is a sum of squares (in the form \(ax^{2}+b\) where \(a = 8\), \(b = 5\) and there are no real - number factors for a sum of non - negative real - valued squares in the real number system), we stop here.

Answer:

\(x(8x^{2}+5)\)