This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: 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. Step 2: Factor out the GCF from each term. Divide each term by 3x^n: For the first term, 15x^2n3x^n = 5x^2n-n = 5x^n. For the second term, 9x^n+13x^n = 3x^(n+1)-n = 3x^1 = 3x. For the third term, (-3x^n)/(3x^n) = -1. Step 3: Write the factored expression. 3x^n(5x^n + 3x - 1) The completely factored expression is: 3x^n(5x^n + 3x - 1) 3 done, 2 left today. You're making progress.