Use a Factor Table to calculate the polynomial product of and
Select a Factor Table with appropriate dimensions.

Ask by Boone Weaver. in the United States

Mar 11,2025

Question

Use a Factor Table to calculate the polynomial product of $$ 4 z+5 $$ and $$ -9 z^{2}-8 z+1 $$ Select a Factor Table with appropriate dimensions.

UpStudy AI · Accepted Answer

$$
\begin{array}{c|ccc}
& -9z^2 & -8z & 1 \ \hline
4z & -36z^3 & -32z^2 & 4z \
5   & -45z^2 & -40z  & 5 \
\end{array}
$$

1. Multiply $$4z$$ by each term of $$-9z^2 - 8z + 1$$:
   - $$4z \times (-9z^2) = -36z^3$$
   - $$4z \times (-8z) = -32z^2$$
   - $$4z \times 1 = 4z$$

2. Multiply $$5$$ by each term of $$-9z^2 - 8z + 1$$:
   - $$5 \times (-9z^2) = -45z^2$$
   - $$5 \times (-8z) = -40z$$
   - $$5 \times 1 = 5$$

3. Combine like terms:
   - The $$z^3$$-term: $$-36z^3$$
   - The $$z^2$$-terms: $$-32z^2 - 45z^2 = -77z^2$$
   - The $$z$$-terms: $$4z - 40z = -36z$$
   - Constant term: $$5$$

Thus, the final product is:

$$
-36z^3 - 77z^2 - 36z + 5
$$
The product of $$4z + 5$$ and $$-9z^2 - 8z + 1$$ is $$-36z^3 - 77z^2 - 36z + 5$$.

Use a Factor Table to calculate the polynomial product of and
Select a Factor Table with appropriate dimensions.

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Use a Factor Table to calculate the polynomial product of and Select a Factor Table with appropriate dimensions.