REVIEW: Polynomials
1. Simplify:
Name:
2. Simplify:
(4cd5)(-2c3)(5cd6)
(+)
(4)(-2)(5) (c)(c3)(c) (d5)(d6)
(5a – 2b + 4) + (9a – 7b – 11)
9a – 7b – 11
14a – 9b – 7
5 11
-40c d
3. Simplify:
(2a3)(4a3) + (5a5)(a)
4. Simplify:
(2)(4)(a3)(a3) + (5)(a5)(a)
8a6 + 5a6
13a6
(5)(2)(x8)(x5) - (6)(3)(x3)(x7)
10x13 – 18x10
5. Simplify: (2a2 – 3a – 5) – (-2a2 – 9a + 7)
2
(-) -2a – 9a + 7
(5x8)(2x5) – (6x3)(3x7)
(change all the signs)
2a2 – 3a – 5
(+) +2a2 + 9a - 7
4a2 + 6a – 12
6. The length of a side of a square is 4x + 5. What is
the area of the square in terms of x?
4x + 5
4x + 5
7. Find the perimeter and area of the shaded region
below:
4x
3x 6x
7x
4x
10x
(4x + 5)(4x + 5)
16x2 + 20x + 20x + 25
16x2 + 40x + 25
8. The sides of a triangle have lengths of
3x – 4, x + 6, and 5x – 7. Find the perimeter of the
triangle in terms of x?
3x
x
5x
9x
–
+
–
–
4
6
7
5
4x + 6x + 3x + 4x + 7x + 10x = 34x
9. Write a polynomial that represents the measure of
∡ABD
+
9x2 – 4x + 2
4x2 + 9x - 8
13x2 + 5x - 6
A
9x2 – 4x + 2
B
C
10. Multiply:
3x2(x2 – 5xy – y2)
(3)(x2)(x2) - (3)(5)(x2)(x)(y) – (3)(x2)(y2)
3x4 – 15x3y – 3x2y2
4x2 + 9x - 8
D
11. Multiply:
(x + 4)(x + 8)
(x)(x) + (x)(8) + (4)(x) + (4)(8)
x2 + 8x + 4x + 32
x2 + 12x + 32
12. Multiply:
(x – 3)(4x2 – x + 3)
(x)(4x2) + (x)(-x) + (x)(3) - (3)(4x2) – (3)(-x) – (3)(3)
4x3 – x2 + 3x - 12x2 + 3x - 9
4x3 - 13x2 + 6x - 9
(4x + 3)(6x – 7)
13. Multiply:
14. Add:
(4x)(6x) + (4x)(-7) + (3)(6x) + (3)(-7)
24x
2
2
24x
28x
+ 18x - 21
15. What is the missing term if the answer is
-5y2 – 15y + 4
(-17y2 + 8y2 – 12y + 7) + (4y2 + ? – 6y – 3)
-5y2 – 18y + 4
- 3y
.
2
-5y – 15y + 4
17. A rectangular painting is bordered on all sides by a
frame. Write an expression to describe the area of the
frame.
3x
x + 2
(+)
-6x3 – 9x2 – 5x + 8
x3 – 5x2 – 6x + 14
- 10x - 21
-9y2 – 12y + 7
(+) 4y2 – 6y – 3)
-5y2 – 18y + 4
(7x3 + 4x2 – x + 6) + (-6x3 – 9x2 – 5x + 8)
(3x + 7)2
16. Multiply:
(3x + 7)(3x + 7)
(3x)(3x) + (3x)(7) + (7)(3x) + (7)(7)
9x2 +
21x +
21x + 49
9x2 + 42x + 49
18. Write an expression that describes the area of the
entire rectangle with the given dimensions?
2x + 3
x
x + 6
3x + 5
(2x + 3)(x + 6)
(x + 2)(3x + 5) – (3x)(x)
(x)(3x) + (x)(5) + (2)(3x) + (2)(5) - (3x)(x)
2
3x +
2
5x
+
2
6x + 10 – 3x
2
3x – 3x + 5x + 6x + 10
(2x)(x) + (2x)(6) + (3)(x) + (3)(6)
2x2 +
12x
+ 3x + 18
2x2 + 15x + 18
11x + 10
19. The measures of the sides of a triangle are given.
Find the perimeter of the triangle.
x2
6x2 – 7x + 5
4x2 – 5x + 4
(+)
x2
6x2 – 7x + 5
11x2 – 12x + 9
Perimeter =
Add all sides
20. Dennis has 2 rectangular plots of land that he is
using for his garden. The first plot has dimensions x
feet by 3x – 7 feet. The second plot has dimensions x –
2 feet by 2x + 4 feet. If he increases each dimension
by 1 foot, which expression shows the combined area of
Dennis’ garden?
(x + 1)(3x – 7 + 1) + (x – 2 + 1)(2x + 4 + 1)
(x + 1)(3x – 6) + (x – 1)(2x + 5)
(x)(3x) + (x)(-6) + (1)(3x) + (1)(-6)
+ (x)(2x) + (x)(5) – (1)(2x) – (1)(5)
3x2 – 6x + 3x – 6
(+) 2x2 + 5x – 2x – 5
5x2 – x + x – 11
21. Multiply:
(4a + 5b)(4a – 5b)
(4a)(4a) + (4a)(-5b) + (5b)(4a) + (5b)(-5b)
16a2 - 20ab +
20ab – 25b2
16a2 – 25b2
22. The perimeter of a picture frame is 78 inches. The
difference between the length of the frame and four
times the width is 4. What is the length of the frame?
2L + 2W = 78
2(4W + 4) + 2W = 78
L – 4W = 4
8W + 8 + 2W = 78
L = 4W + 4
10W + 8 = 78
L = 4(7) + 4
10W = 70
L = 32
23. A clothing store sells t-shirts and jeans. The store
pays its supplier $3.75 per t-shirt and $6.50 per pair of
jeans, plus a shipping fee per order of $140. The store
then charges the customer $15 per t-shirt and $39.50
per pair of jeans. Write the expression that represents
the store’s profit if it sells x t-shirts and y jeans?
W = 7
Repeat number 20 - OOPS
Revenue – Cost = Profit
Revenue:
15.00x + 39.50y
Cost:
3.75x + 6.50y
Profit:
11.25x + 33y
25. Christine is selling tickets at a museum. She knows
that she has sold at least 48 tickets. The adult tickets
cost 10 dollars and the children’s tickets cost 8 dollars.
If she knows she has sold no more than $640 worth of
tickets, list one possible combination? Graph the
system of inequalities.
A + C ≥ 48
C ≥ -A + 48
26. Max invested a total of $2000 in two simple
interest accounts. Account J earns 3% interest and
Account K earns 5% interest. Max earned a total of
$85 interest after one year. How much did Max invest
in each account?
J + K = 2000
.03J + .05K = 85
J = 2000 - K
.03(2000- K) + .05K = 85
60 - .03K + .05K = 85
60 + .02K = 85
.02K = 25
10A + 8C ≤ 640
K = 1250
J = 2000 – 1250
8C ≤ -10A + 640
C ≤
−𝟓
𝟒
J = 750
A + 80
(32, 24)
27. Write two points in the solution to the system of
inequalities and two points not in the solution.
28. Find the solution of the system by graphing.
y = 2x + 5
y ≥ 3x + 1
y ≤ -2x + 11
Solution: (-2, 4), (-4, 6)
NOT:
𝟏
y = − 𝟐x
What is the solution of the system?
(-2, 1)
(2, 4), (8, 6)
29. Joan joins a fitness club that has a membership fee
of $5 plus $20 per month. Kaye’s club has a fee of $50
and charges $5 per month. In how many months will the
clubs cost the same?
Joan: 20m + 5
Kaye: 5m + 50
20m + 5 = 5m + 50
- 5 =
- 5
20m = 5m + 45
- 5m = -5m
.
15m = 45
15
15
m = 3
In 3 months the clubs will cost the same.
30. Find the solution for the system of equations.
4y = 2x
4y – 2x = 0
4y = 2x
𝟏
y = x
𝟐
4y – 2x = 0
4y = 2x
𝟏
y = x
𝟐
They are the same line.
Infinite solutions