Question

In the following exercises, multiply. Use either Method.

$\left(6r+1\right)\left(r^2-7r-9\right)$

Short answer

The product of the given polynomials is$6r^3-41r-61r-9$

Step-by-step solution

Step 1. Given Information

The given polynomials are$\left(6r+1\right)\left(r^2-7r-9\right)$

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:

$$\begin{gathered} \left(6r+1\right)\left(r^2-7r-9\right)=6r\left(r^2-7r-9\right)+1\left(r^2-7r-9\right) \\ \left(6r+1\right)\left(r^2-7r-9\right)=6r^3-42r^2-54r+r^2-7r-9 \\ \left(6r+1\right)\left(r^2-7r-9\right)=6r^3-41r-61r-9 \end{gathered}$$

Step 3. Conclusion

The product of the polynomials is$6r^3-41r-61r-9$