Factor the expression. Please show your work
2x^2 + 14× + 24
To factor the expression 2x^2 + 14x + 24, we need to find two binomials that when multiplied together will give us the original expression.
First, we can see that all three terms in the expression have the common factor of 2. So we can factor out the common factor of 2:
2(x^2 + 7x + 12)
Now we need to find two binomials that will give us x^2 + 7x + 12 when multiplied together. Let's try to fill in the binomials in the form (x + ?)(x + ?):
(x + ?)(x + ?) = x^2 + 7x + 12
To find the two missing values, we need to think of two numbers that multiply to give us 12 and add up to give us 7. The two numbers are 3 and 4. Therefore, we can write:
(x + 3)(x + 4)
Now we can put it all together:
2(x + 3)(x + 4)
This is the factored form of the expression 2x^2 + 14x + 24.