Question

1. the length of a rectangle is represented by $x^{2}+3x + 2$, and the width is represented by $4x$. (a) express the perimeter of the rectangle as a trinomial. (b) express the area of the rectangle as a trinomial.

Explanation:

Step1: Recall perimeter formula

Perimeter \( P = 2(\text{length} + \text{width}) \)

Step2: Substitute length and width

\( P = 2[(x^2 + 3x + 2) + 4x] \)

Step3: Simplify inside parentheses

\( (x^2 + 3x + 2) + 4x = x^2 + 7x + 2 \)

Step4: Multiply by 2

\( P = 2(x^2 + 7x + 2) = 2x^2 + 14x + 4 \)

Step5: Recall area formula

Area \( A = \text{length} \times \text{width} \)

Step6: Substitute and expand

\( A = (x^2 + 3x + 2)(4x) = 4x^3 + 12x^2 + 8x \)

Answer:

(a) \( 2x^2 + 14x + 4 \)
(b) \( 4x^3 + 12x^2 + 8x \)