Question

which of the following represents the area of a rectangle whose length is 3x + 5 and whose width is x - 2?
3x² - x - 10
3x² - 10
3x² + x - 10
3x² - 11x - 10

Explanation:

Step1: Recall area formula

The area $A$ of a rectangle is $A = \text{length}\times\text{width}$. Here, length $l=3x + 5$ and width $w=x - 2$. So $A=(3x + 5)(x - 2)$.

Step2: Expand the product

Using the FOIL method:
First terms: $3x\times x=3x^{2}$
Outer terms: $3x\times(- 2)=-6x$
Inner terms: $5\times x = 5x$
Last terms: $5\times(-2)=-10$
Then $A=3x^{2}-6x + 5x-10$.

Step3: Combine like - terms

Combining $-6x$ and $5x$ gives $-x$. So $A = 3x^{2}-x - 10$.

Answer:

$3x^{2}-x - 10$