Question

$8w - 4$
what is the degree of the polynomial product?
enter the coefficients for each term in the product of $8w - 4$ and $3w^{2}-w - 6$.
enter 0 as the coefficient of any terms not in the product.
$()w^{3}+()w^{2}+()w+()$
options: $8w$, $24w^{3}$, $-8w^{2}$, $-48w$, $-4$, $-12w^{2}$, $4w$, $24$

Explanation:

Step1: Multiply polynomials via distribution

$$(8w - 4)(3w^2 - w - 6) = 8w(3w^2 - w - 6) - 4(3w^2 - w - 6)$$

Step2: Expand each term

$$= 24w^3 - 8w^2 - 48w - 12w^2 + 4w + 24$$

Step3: Combine like terms

$$= 24w^3 + (-8w^2 -12w^2) + (-48w + 4w) + 24$$
$$= 24w^3 -20w^2 -44w + 24$$

Step4: Identify polynomial degree

The highest power of $w$ is 3.

Answer:

Degree of the polynomial product: 3
Coefficients:
$24w^3 + (-20)w^2 + (-44)w + (24)$