Final answer:
The quadratic expression 2x^2 + 16x + 24 can be factored by first taking out the greatest common factor, which is 2, and then factoring the remaining quadratic to obtain 2(x + 2)(x + 6).
Step-by-step explanation:
The expression 2x^2 + 16x + 24 is a quadratic expression that we want to factor. To factor this expression, look for a greatest common factor (GCF) first, which in this case is 2. So, we can rewrite the expression as:
2(x^2 + 8x +12)
Now, we need to factor the quadratic inside the parentheses. We look for two numbers that multiply to give us the constant term, 12, multiplied by the coefficient of x^2, which is 1, so just 12, and also add up to give us the coefficient of x, which is 8. Those two numbers are 2 and 6.
The expression inside the parentheses can now be rewritten as:
(x + 2)(x + 6)
Hence, the factored form of the quadratic expression is:
2(x + 2)(x + 6)