What is the expression in factored form?
2x2+16x+24
The expression 2x^2 + 16x + 24 cannot be factored further as the coefficient of x^2 is not equal to 1 and there are no common factors among the terms.
To find the expression in factored form, we need to factor out the common factors, if any, from the given expression. In this case, we can first look for any common factors. The expression 2x^2 + 16x + 24 has a common factor of 2. We can factor out 2 from each term:
2(x^2 + 8x + 12)
Now, we need to figure out how to factor the remaining quadratic expression x^2 + 8x + 12. We need to find two numbers that multiply to give 12 (the constant term) and add up to give 8 (the coefficient of the x term).
The numbers that satisfy these conditions are 6 and 2. This means we can factor the expression as follows:
2(x + 6)(x + 2)
So, the expression in factored form is 2(x + 6)(x + 2).
To find the expression in factored form, we need to factor the given quadratic expression.
Step 1: Look for a common factor. In this case, there is no common factor among all three terms.
Step 2: We need to find two numbers that multiply to give the product of the leading coefficient (2) and the constant term (24), which is 48, and add up to the coefficient of the middle term (16). In this case, the numbers are 4 and 12.
Step 3: Rewrite the middle term using the two numbers found in step 2:
2x^2 + 4x + 12x + 24
Step 4: Group the terms:
(2x^2 + 4x) + (12x + 24)
Step 5: Factor out the greatest common factor from each group:
2x(x + 2) + 12(x + 2)
Step 6: Notice that (x + 2) is a common factor in both terms.
Step 7: Factor out (x + 2) from both terms:
(x + 2)(2x + 12)
Therefore, the expression 2x^2 + 16x + 24 in factored form is (x + 2)(2x + 12).