What is the expression in factored form?2x2+16x+24 show work
To factor the expression 2x^2 + 16x + 24, we can first look for common factors among the coefficients. The greatest common factor of 2, 16, and 24 is 2. Dividing each term by 2, we get:
2x^2 / 2 = x^2
16x / 2 = 8x
24 / 2 = 12
So the expression in factored form is:
2x^2 + 16x + 24 = 2(x^2 + 8x + 12)
Next, we need to factor the expression inside the parentheses:
x^2 + 8x + 12
To do this, we need to find two numbers that multiply to give 12 and add up to 8. The numbers 6 and 2 satisfy these conditions, so we can factor the expression as:
x^2 + 8x + 12 = (x + 6)(x + 2)
Putting it all together, we have:
2x^2 + 16x + 24 = 2(x + 6)(x + 2)