Question

Factor completely.
2d^2+7d+6

Answer 1

To factor the quadratic expression \( 2d^2 + 7d + 6 \), we need to find two numbers that multiply to the product of the coefficient of \( d^2 \) and the constant term (which is \( 2 \times 6 = 12 \)) and add up to the coefficient of \( d \) (which is \( 7 \)).

The two numbers that multiply to \( 12 \) and add up to \( 7 \) are \( 3 \) and \( 4 \).

Now, we can rewrite the middle term \( 7d \) using \( 3d \) and \( 4d \):

\[
2d^2 + 3d + 4d + 6
\]

Next, we group the terms:

\[
(2d^2 + 3d) + (4d + 6)
\]

Now, factor out the common factors in each group:

\[
d(2d + 3) + 2(2d + 3)
\]

Now we can factor out the common binomial factor \( (2d + 3) \):

\[
(2d + 3)(d + 2)
\]

Thus, the completely factored form of \( 2d^2 + 7d + 6 \) is:

\[
(2d + 3)(d + 2)
\]