Question

which polynomial represents the area of the rectangle? o 3x^2 - 2x - 5 o 3x^2 - 5 o 3x^2 + 2x - 5 o 3x^2 - 8x - 5

Explanation:

Step1: Recall area formula for rectangle

The area $A$ of a rectangle is given by $A = l\times w$, where $l$ is the length and $w$ is the width. Here, $l = 3x - 5$ and $w=x + 1$.

Step2: Multiply the binomials

Use the FOIL method: $(3x-5)(x + 1)=3x\times x+3x\times1-5\times x - 5\times1$.

Step3: Simplify the expression

$3x\times x+3x\times1-5\times x - 5\times1=3x^{2}+3x-5x - 5=3x^{2}-2x - 5$.

Answer:

$3x^{2}-2x - 5$