Factor the expression. Please show your work 2x² + 14x + 24
To factor the expression 2x² + 14x + 24, we can start by looking for common factors. In this case, the common factor is 2. Factoring out 2, we get:
2(x² + 7x + 12)
Now we need to factor the quadratic trinomial inside the parentheses, x² + 7x + 12. To do so, we need to find two numbers that multiply to give 12 and add up to give 7. These numbers are 3 and 4. Therefore, we can factor the quadratic trinomial as:
(x + 3)(x + 4)
Putting it all together, the expression 2x² + 14x + 24 can be fully factored as:
2(x + 3)(x + 4)