Question

In the following exercises, multiply. Use either Method.

$\left(3q+1\right)\left(q^2-4q-5\right)$

Short answer

The product of the given polynomials is$3q^3-11q^2-19q-5$

Step-by-step solution

Step 1. Given Information

The given polynomials are$\left(3q+1\right)\left(q^2-4q-5\right)$

The product is to be determined using any method i.e. either the Distributive Property or the Vertical Method.

Step 2. Using distributive property

According to distributive property:

$$\begin{gathered} \left(3q+1\right)\left(q^2-4q-5\right)=3q\left(q^2-4q-5\right)+1\left(q^2-4q-5\right) \\ \left(3q+1\right)\left(q^2-4q-5\right)=3q^3-12q^2-15q+q^2-4q-5 \\ \left(3q+1\right)\left(q^2-4q-5\right)=3q^3-11q^2-19q-5 \end{gathered}$$

Step 3. Conclusion

The product of the polynomials is$3q^3-11q^2-19q-5$