Problem 37 - Algebra 1: Concepts and Skills

Question

Factor the expression completely. \(2 y^{3}-10 y^{2}-12 y\)

Step-by-Step Solution

Answer

The complete factorization of the given expression is \(2y(y-6)(y+1)\).

Step 1: Identify the GCD

First, identify the greatest common divisor (GCD) among all terms. Looking at the expression, each term can be divided by \(2y\). So the GCD is \(2y\).

Step 2: Factor out the GCD

Next, factor out the GCD from each term of the polynomial. This means, divide each term of the polynomial by the GCD and write the polynomial as the product of the GCD and the result of divisions. So you get \(2 y (y^{2}-5 y-6)\).

Step 3: Factor the polynomial within the parenthesis

The polynomial in the parenthesis can still be factored. The expression \(y^{2}-5 y-6\) Is a quadratic polynomial and can be factored into two binomial expressions as such:\((y-6)(y+1)\). This leaves us with the final answer: \(2y(y-6)(y+1)\)