Question

Which of these shows the factor of 2p^3 + 5p^2 + 6p + 15 when you factor by grouping?

a. (2p + 3)(p^2 + 2p + 5)
b. (2p + 5)(p^2 + 3p + 3)
c. (2p + 3)(p^2 + 3p + 5)
d. (2p + 5)(p^2 + 2p + 3)

Answer 1

The polynomial 2p^3 + 5p^2 + 6p + 15 is factored by grouping and the correct factored form is (2p + 5)(p^2 + 3p + 3), which corresponds to option b.

Step-by-step explanation:

Factor by grouping involves combining terms in a polynomial so that each group has a common factor. In the polynomial 2p^3 + 5p^2 + 6p + 15, we can group the terms as follows:

• (2p^3 + 5p^2) + (6p + 15)

First, factor out the GCF (Greatest Common Factor) from each group:

• p^2(2p + 5) + 3(2p + 5)

As you can see, both groups now have a common binomial factor (2p + 5). We can factor this binomial out:

• (2p + 5)(p^2 + 3p + 3)

Therefore, the correctly factored form of the polynomial is option b. (2p + 5)(p^2 + 3p + 3).