Question

question use the box method to distribute and simplify (-x + 4)(x³ + 3 + 3x⁴ + 5x²) (-x + 4)(x³ + 3 + 3x⁴ + 5x²) rows: 0 columns: 0 answer attempt 1 out of 2 you must answer all questions above in order to submit. show examples

Explanation:

Step1: Set up box (2 rows, 5 cols)

First, identify the terms of each polynomial:
Row terms: $-x, 4$
Column terms: $3x^4, x^3, 5x^2, 6x, 3$

Step2: Fill box with products

	$3x^4$	$x^3$	$5x^2$	$6x$	$3$
$4$	$12x^4$	$4x^3$	$20x^2$	$24x$	$12$

Step3: Combine like terms

1. $x^5$ term: $-3x^5$
2. $x^4$ terms: $-x^4 + 12x^4 = 11x^4$
3. $x^3$ terms: $-5x^3 + 4x^3 = -x^3$
4. $x^2$ terms: $-6x^2 + 20x^2 = 14x^2$
5. $x$ terms: $-3x + 24x = 21x$
6. Constant term: $12$

Step4: Write simplified polynomial

Arrange terms by descending degree:
$-3x^5 + 11x^4 - x^3 + 14x^2 + 21x + 12$

Answer:

$-3x^5 + 11x^4 - x^3 + 14x^2 + 21x + 12$

Box Setup Note:

Rows = 2 (for $-x$ and $4$), Columns = 5 (for $3x^4, x^3, 5x^2, 6x, 3$)