# Polynomial Word Problems – Notes

```Name:________________________ Per:______
Chapter 8 Test Review
1. If y varies directly with x cubed, and y = 3 when x = 2, find y when x = 4.
k =________
new equation:____________________
y =________
2. If y varies inversely with x, and x = 2 when y =12, find y when x = 8.
k =________
new equation:____________________
y =________
3. a. _____________ a. Is the relationship between the values in the table direct variation,
b. _____________ inverse variation, or neither? b. Write an equation to model the variation.
4. a. _____________ a. Is the relationship between the values in the table direct variation,
b. _____________ inverse variation, or neither? b. Write an equation to model the variation.
For problems 5 – 10, a) find the restrictions, and b) simplify.
6 x3 3xy
5.

y2
2
2u  6
u3  u

6. 2
u  2u  3 u 2  u  2
x 2  25
7.
10 x  50
x
y
1
5
3
15
7
35
x
y
1
36
3
12
6
6
8.
u2  9 u  3

u  2 u2  4
9.
4x3 y 2 z 5
10.
20 x 3 y 7 z
6 x  48

x 2  5 x  24 3x 2  8 x  3
11. Why is it necessary to find restrictions when simplifying rational expressions?
12. Write your own expression that would simplify to
x2  9
x3
5x
For problems 13 – 16, circle the choice that CANNOT be a factor of the given polynomial.
13. x2 – 9x + 20
a. x - 4
b. x + 5
c. x - 5
14. 8x3y – 50xy3
a. 2xy2
b. 2x + 5y
c. 2x – 5y
15. x3 – 4x2y – 21xy2
a. x – 7y
b. x
c. x – 3y
16. 15x4 – 27x3y – 6x2y2
a. 3x2
b. x – 2y
c. 6x2
17. 8y3 - 27
a. 2y - 3
b. 4y2 – 6y + 9
c. 4y2 + 6y + 9
3
3
b. y = x3 c. 24
8
8
4. a. inverse b. xy = 36 OR y =
7. a. x ≠ -5 b.
x5
10
2.a. 24 b. xy = 24 OR y =
36
4x 2
5. a. x ≠ 0, y ≠ 0 b.
x
y3
8. a. u ≠ -2, -3 b. (u – 3)(u – 2)
1
6
10. a. x ≠ -3,  , 3, 8 b.
3
3x  1
xy  3 y
will vary, but an example is
5 xy
24
c. 3
x
3. a. direct b. y = 5x
6. a. u ≠ -3, -1, 1, 2 b.
9. a. x ≠ 0, y ≠ 0, z ≠ 0 b.
2u
u2
z4
5y 5
11. So that no denominator may have the value of 0 12. Answers
13. b
14. a
15. c
16. c
17.
b
```