What is the expression in factored form? 2x^2+16x +24
The expression in factored form is 2(x + 2)(x + 6).
show the steps
To factor the given expression 2x^2 + 16x + 24, we first need to find the factors of 2*24 = 48 that add up to 16 (the coefficient of the middle term).
The factors of 48 that add up to 16 are 4 and 12.
Next, we rewrite the middle term 16x as the sum of these two terms:
2x^2 + 4x + 12x + 24
Now, we group the terms and factor out the common factors:
2x(x + 2) + 12(x + 2)
Finally, we factor out the common factor of (x + 2) from both terms:
(x + 2)(2x + 12)
And simplifying further, we get:
(x + 2)(2)(x + 6)
2(x + 2)(x + 6)
Therefore, the factored form of the expression 2x^2 + 16x + 24 is 2(x + 2)(x + 6).