Exercise 36 Page 421

Let's take a look at the given expression. 2/5x + 16 We want to use the Distributive Property in reverse to factor the expression. To do so, we first want to write the constant as an improper fraction with a denominator of 5. Let's do it!

16

WriteAsFrac

Write as a fraction

16/1

ExpandFrac

a/b=a * 5/b * 5

16 * 5/1* 5

Multiply

Multiply

80/5

Now, notice that the numerator of the fraction to the left of the variable x is 2. Let's factor the numerator of our improper fraction so that one of the factors is 2. Then, move the second factor to the right of the fraction.

80/5

Rewrite

Rewrite 80 as 2 * 40

2 * 40/5

MovePartNumRight

a* b/c=a/c* b

2/5 * 40

Let's rewrite our expression using the changes we made to the constant term. 2/5x + 16 ⇔ 2/5x + 2/5 * 40 Finally, let's factor out the fraction 2 5 in our expression. 2/5x + 2/5 * 40 ⇔ 2/5(x+40)