Question

factor out the greatest common factor.
$2x^{10} + x^6 - 5x^4 + x$
$x^{?} \left(2x^9 + x^5 - 5x^3 + 1\
ight)$

Explanation:

Step1: Identify the GCF of coefficients and variables

For the terms \(2x^{10}\), \(x^{6}\), \(-5x^{4}\), and \(x\):

• The greatest common factor (GCF) of the coefficients \(2\), \(1\), \(-5\), and \(1\) is \(1\).
• For the variable part, we look at the lowest power of \(x\) among the terms. The powers of \(x\) are \(10\), \(6\), \(4\), and \(1\). The lowest power is \(1\) (from the term \(x = x^{1}\)). So the GCF of the variable part is \(x^{1}=x\).

Step2: Factor out the GCF

When we factor out \(x\) from each term:

• \(2x^{10}\div x = 2x^{9}\)
• \(x^{6}\div x = x^{5}\)
• \(-5x^{4}\div x=-5x^{3}\)
• \(x\div x = 1\)

So the exponent of \(x\) that we factor out is \(1\).

Answer:

\(1\)