Question

use the box method to distribute and simplify $(-x - x^3 + 1 - x^2)(-x - 3)$. drag and drop the terms to the correct locations of the table. $(-x - x^3 + 1 - x^2)(-x - 3)$ rows: 0 columns: 0

Explanation:

Step1: Rearrange polynomials by degree

First polynomial: $-x^3 -x^2 -x + 1$
Second polynomial: $-x - 3$

Step2: Set up box dimensions

Rows = number of terms in first polynomial = 4
Columns = number of terms in second polynomial = 2

Step3: Fill box with products

	$-x$	$-3$
$-x^2$	$(-x^2)(-x)=x^3$	$(-x^2)(-3)=3x^2$
$-x$	$(-x)(-x)=x^2$	$(-x)(-3)=3x$
$1$	$(1)(-x)=-x$	$(1)(-3)=-3$

Step4: Combine like terms

$x^4 + (3x^3+x^3) + (3x^2+x^2) + (3x-x) -3$
$=x^4 + 4x^3 + 4x^2 + 2x -3$

Answer:

Box setup:

Rows: 4, Columns: 2

Filled table:

	$-x$	$-3$
$-x^2$	$x^3$	$3x^2$
$-x$	$x^2$	$3x$
$1$	$-x$	$-3$

Simplified polynomial:

$x^4 + 4x^3 + 4x^2 + 2x - 3$