Exercise 10 Page 86

We want to determine the width of a rectangle whose length and area are given. Therefore, we will use the formula for the area of a rectangle. A=l wWe know that the area is 2x^2-x-15 square units and that the length is 2x+5 units. Let's multiply the expression for the length by the given options and check which multiplication results in the given area. We will start by multiplying 2x+5 by x-5, which is the expression given in choice F.

2x^2-x-15? =(2x+5)(x-5)

Distr

Distribute (x-5)

2x^2-x-15? =2x(x-5)+5(x-5)

▼

Distribute 2x & 5

Distr

Distribute 2x

2x^2-x-15? =2x^2-10x+5(x-5)

Distr

Distribute 5

2x^2-x-15? =2x^2-10x+5x-25

AddTerms

Add terms

2x^2-x-15≠ 2x^2-5x-25 *

If we multiply the expression given in choice F by the length, we do not obtain the given area. Therefore, this choice is not correct. Let's follow a similar procedure and multiply the length by the expressions given in the other choices.

Choice	Expression	Multiply	Simplify
F	x-5	2x^2-x-15? =(2x+5) (x-5)	2x^2-x-15≠ 2x^2-5x-25
G	x+3	2x^2-x-15? =(2x+5) (x+3)	2x^2-x-15≠ 2x^2+11x+15
H	x-3	2x^2-x-15? =(2x+5) (x-3)	2x^2-x-15= 2x^2-x-15
J	2x-3	2x^2-x-15? =(2x+5) (2x-3)	2x^2-x-15≠ 4x^2+4x-15

Therefore, the correct option is H.