Question

use a factor table to calculate the polynomial product of $-7w^2 - 8w - 6$ and $2w^2 + 8w - 7$.
select a factor table with appropriate dimensions.
○ 1x2
○ 2x1
○ 1x3
○ 3x1
○ 2x2
○ 2x3
○ 3x2
○ 3x3

Explanation:

Step1: Identify factor table dimensions

First polynomial: $-7w^2 -8w -6$ (3 terms), second polynomial: $2w^2 +8w -7$ (3 terms). So the factor table is 3x3.

Step2: Set up and fill the table

Multiply each term from the first polynomial by each term from the second polynomial:

	$2w^2$	$8w$	$-7$
$-8w$	$-8w \times 2w^2 = -16w^3$	$-8w \times 8w = -64w^2$	$-8w \times (-7) = 56w$
$-6$	$-6 \times 2w^2 = -12w^2$	$-6 \times 8w = -48w$	$-6 \times (-7) = 42$

Step3: Combine like terms

Combine terms with the same exponent of $w$:

• $w^4$ term: $-14w^4$
• $w^3$ terms: $-56w^3 -16w^3 = -72w^3$
• $w^2$ terms: $49w^2 -64w^2 -12w^2 = -27w^2$
• $w$ terms: $56w -48w = 8w$
• Constant term: $42$

Step4: Assemble the final polynomial

Combine all simplified terms in descending order of exponents.

Answer:

Polynomial Product:

$-14w^4 -72w^3 -27w^2 +8w +42$

Correct Factor Table Dimension:

3x3