Problem 23 - Algebra 1: Concepts and Skills

Question

Find the greatest common factor of the terms and factor it out of the expression. \(15 x^{3}-5 x^{2}-10 x\)

Step-by-Step Solution

Answer

The factored form of the given expression \(15x^3 - 5x^2 - 10x\) is \(5x(3x^2 - x - 2)\).

Step 1: Identify the Coefficients and Powers

The coefficients of the terms of the expression are 15, -5, -10 while the powers of x are 3, 2, 1 respectively.

Step 2: Find the GCF of the Coefficients

The GCF of the coefficients 15, -5, -10 is 5.

Step 3: Find the GCF of the Powers

The GCF of the powers 3, 2, 1 is 1.

Step 4: Factorize the Expression Using the GCF

Combine the GCF of coefficients and powers, we get 5x. Factoring the expression by 5x, we get \(5x(3x^2 - x - 2)\).