(2x%5E2%2B4x)-factor.jpeg "(x^2+x-6)(2x^2+4x) Factor")
Factoring the Expression: (x^2+x-6)(2x^2+4x)
This problem involves factoring a product of two quadratic expressions. Let's break it down step-by-step:
Factoring the Individual Expressions
1. Factoring (x^2 + x - 6):
- Find two numbers that multiply to -6 and add up to 1 (the coefficient of the x term).
- These numbers are 3 and -2.
- Therefore, (x^2 + x - 6) factors as (x + 3)(x - 2).
2. Factoring (2x^2 + 4x):
- Factor out the greatest common factor (GCF), which is 2x.
- This leaves us with 2x(x + 2).
Combining the Factored Expressions
Now we have the factored form of the original expression:
(x^2 + x - 6)(2x^2 + 4x) = (x + 3)(x - 2) * 2x(x + 2)
Simplifying the Expression
We can further simplify the expression by rearranging the terms:
(x + 3)(x - 2) * 2x(x + 2) = 2x(x + 3)(x - 2)(x + 2)
This is the fully factored form of the original expression.
Summary
By factoring each quadratic expression individually and then combining them, we were able to completely factor the expression (x^2 + x - 6)(2x^2 + 4x) into:
2x(x + 3)(x - 2)(x + 2)