Question

question 5 (1 point) (01.08) which of the following represents the area of a rectangle whose length is 3x + 5 and whose width is x - 2?

a \t3x² - x - 10

b \t3x² - 10

c \t3x² + x - 10

d \t3x² - 11x - 10

Explanation:

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is given by the product of its length and width, i.e., \( A=\text{length}\times\text{width} \). Here, length is \( 3x + 5 \) and width is \( x - 2 \), so we need to compute \( (3x + 5)(x - 2) \).

Step2: Apply distributive property (FOIL method)

First, multiply the First terms: \( 3x\times x = 3x^{2} \).
Then, the Outer terms: \( 3x\times(-2)=-6x \).
Next, the Inner terms: \( 5\times x = 5x \).
Finally, the Last terms: \( 5\times(-2)=-10 \).
Now, combine these terms: \( 3x^{2}-6x + 5x-10 \).

Step3: Combine like terms

Combine the \( x \)-terms: \( -6x+5x=-x \). So the expression becomes \( 3x^{2}-x - 10 \).

Answer:

a. \( 3x^{2}-x - 10 \)