Question

$7z^{2}-3z-3$
$4z$
$7z^{2}$
$-3z$
$-3$
$28z^{3}$
$-12z^{2}$
$-12z$

1. what is the degree of the polynomial product?
2. enter the coefficients for each term in the product of $4z$ and $7z^{2}-3z-3$. enter 0 as the coefficient of any terms not in the product.

$(\quad)z^{3}+(\quad)z^{2}+(\quad)z+(\quad)$

Explanation:

Step1: Multiply polynomials via distribution

$$4z \times (7z^2 - 3z - 3) = 4z \times 7z^2 + 4z \times (-3z) + 4z \times (-3)$$

Step2: Calculate each term

$$= 28z^3 - 12z^2 - 12z$$

Step3: Identify highest exponent

The term $28z^3$ has exponent 3, the highest in the product.

Step4: Fill coefficient blanks

Match coefficients to the standard polynomial form: $(\boldsymbol{28})z^3 + (\boldsymbol{-12})z^2 + (\boldsymbol{-12})z + (\boldsymbol{0})$

Answer:

Degree of the polynomial product: 3
Filled coefficients: $28z^3 + (-12)z^2 + (-12)z + 0$