Factor the expression: 15x2n + 9xⁿ+1 − 3xⁿ

Question

ScanSolve AI Tutor · Accepted Answer

This is the same question you sent previously. Here is the step-by-step solution again:

Identify the greatest common factor (GCF) of the terms.
The given expression is $15x^{2n} + 9x^{n+1} - 3x^n$ .
First, find the GCF of the numerical coefficients: 15, 9, and 3. The greatest common divisor of these numbers is 3.
Next, find the GCF of the variable terms: $x^{2n}$ , $x^{n+1}$ , and $x^n$ . The lowest power of $x$ present in all terms is $x^n$ .
So, the GCF of the entire expression is $3x^n$ .
Factor out the GCF from each term.
Divide each term by $3x^n$ :
For the first term:
$\frac{15x^{2n}}{3x^n} = 5x^{2n-n} = 5x^n$
For the second term:
$\frac{9x^{n+1}}{3x^n} = 3x^{(n+1)-n} = 3x^1 = 3x$
For the third term:
$\frac{-3x^n}{3x^n} = -1$
Write the factored expression.
Combine the GCF with the results from Step 2:
$3x^n(5x^n + 3x - 1)$

Factor the expression: 15x2n + 9xⁿ+1 - 3xⁿ