© 2016 Shmoop University, Inc. All rights reserved.
Polynomial Division and Rational Expressions

Polynomial Division and Rational Expressions

Polynomial Division and Rational Expressions: Proportion Control True or False

1. For the equation , the value x = 0

-> is neither a solution nor an extraneous solution.

2. Which value is an extraneous solution to the equation 


-> x = 1

3. The equation


-> solutions at x = 0, x = 3, and x = -5.

4. If y = 4x, then -> y is directly proportional to x.
5. If y = 4x2 + 2, then -> y is directly proportional to x.
6. A rectangle's length is three feet more than five times its width. The area of the rectangle is 2 square feet. In units of feet, what is the length of the rectangle? -> x = 5
7. The two triangles shown below (the big one and the smaller one sitting inside of it) are similar. Among other things, this means the ratio of height to base is the same for both triangles. What is the height of the larger triangle?


8. The number of butterflies Mariposa gets in her yard is proportional to the number of butterfly bushes she plants. Obviously, we're talking about the butterfly plant, not butterflies the insect. Everyone knows those come from trees. If planting 7 bushes gets her 91 butterflies, how many bushes must she plant to get 130 butterflies? -> 10
9. A horror movie has a crazy cat lady character who also owns a lot of birds. The ratio of cats to birds in her house is 4:7. If there are 512 legs in her house, how many birds does she have? The lady, by the way, has no legs of her own. We told you it was a horror movie... -> 17
10. y is inversely proportional to x with constant 9. If three less than half of y is five greater than y, what is x? -> -7