Question

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

Explanation:

Step1: Identify the GCF of terms

The terms are \(2x^{10}\), \(x^6\), \(-5x^4\), \(x\). The GCF of the coefficients (2, 1, -5, 1) is 1. For the variable part, the lowest power of \(x\) is \(x^1\) (i.e., \(x\)). So the GCF is \(x\).

Step2: Factor out the GCF

Divide each term by \(x\):

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

So factoring out \(x\) gives \(x(2x^9 + x^5 - 5x^3 + 1)\).

Answer:

\(x\)