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Math 9
Unit 4
Polynomials
Review Portfolio
Name:___________________
Home Room______________
Part A Practice MC and NR
/4
Show work where applicable
Check your answer
Part B Practice Written Response
/6
Show your work
Check your answer
Total
/10
Study Guide
Definitions you need to know
Constant
Distributive Property
Numerical Coefficient
Variable
Literal Coefficient
Term
Like Terms
Expression
Polynomial
Monomial
Binomial
Trinomial
Degree
Standard Form
Additive Inverse
Operations that you need to be able to do
Operation
Adding polynomials (with tiles as well)
Subtracting polynomials (with tiles as well)
*Additive Inverse
Multiplying and Dividing Monomials
Multiplying Polynomials by a Monomial (with tiles as well)
Dividing Polynomials by a Monomial
Definitions of terms
Part A
Practice Multiple Choice and Numerical Response
1. Which expressions are polynomials?
A.
B.
C.
D.
1, 2, 3, and 4
1 and 4 only
1, 2, and 4
1, 3, and 4
1.
7n  8n  9
2.
3 n3
3.
3
x
4.
3w 3  12
Answers
MC
1.
2.
3.
4.
5.
NR
1.
2
2. What is the perimeter of the figure expressed as an algebraic
expression?
4m 2 n 4
B. 4m  n 4
C. 4m  4n
A.
D. 4m 2  n 4
3. Which model represents the polynomial 2n 2  2n  4 ?
A.
B.
C.
D.
4. Which algebraic expression represents the difference modeled by the
tiles?
A.
B.
C.
D.
 2x
 2x
 2x
 2x
2
2
2
2


 3x  4  x  x  1
 3x  4  x  x  1
 3x  4 3x  5x  7
 3x  4  x 2  x  1
2
2
2
5. The diagram represents a swimming pool surrounded by a
measurements are in square meters. What is the area of
A.
8a 2b 2
m2
B.
30ab2
m2
C. 42ab2
m2
patio. All
the patio?
D. 4ab  2b m2
Numerical Response
1. What is the coefficient of the x 2 term after simplifying?
17x  4x   x
2
2

 8x  3x 2  5x

Part B
Practice Written Response
1. Complete the table
Algebra
Tiles
Simplified
Algebraic
Form
3x
Name
Monomial
Substitute
x2
32  6
a.
b.
2. Identify polynomial type and degree
Polynomial
Type
Degree
a.
x 2 yz  2 yz
b.
b 2 x 3  2x 2  4xy 2
c.
5
3. Write a polynomial to represent the perimeter of the figure below and name it.
Polynomial _______________
Name ______________
4. Add the following polynomials.
a.
5x
2

 3y 2  x 2  4 y

b.
3x 2  7 x  5
 x2  x 3
Substitute
x  4
3 4  12
5. Subtract the following polynomials
a.
3x
2


 5x  7  2 x 2  4 x  9
b.
8x 2  2 x  1
3x 2  x  7
6. Simplify, then evaluate for x  2
a.
4x
2


 3x  x 2  2x  3x 2  x

7. Find the expression for each of the missing dimensions for
the figure, shown left, if the perimeter is 7 x  9 .
8. Simplify.
a.

4 x 2  2 xy 2 z

b.

 s 2 t 2 3s 3t 2

9. Simplify. Positive exponents only
a.
20 x 5 y 3
5x 4 y 6
b.
9ab 4
c.
 45y   5 y 
6
4
45 a 2 b 4
10. The rectangle has an area of 28x 5 y 2 . Find the missing
dimension for the missing side.
7x 3 y
?
11. Expand and simplify
a.
 x2 x  3  x  5
c.
 3a 2a 2  4a  2

b.
5 y5 y  7  3 y3 y  5
b.
 9a 4  12 a 3  15 a 2

12. Simplify
a.
15 x 5  20 x 4  5 x 2
10 x 3
13. Write an expression for the area of the figure shown
14. Simplify
5 y  2 y2 y  3
 3a 2
Answers
Part A
MC
1.
B
5.
B
NR
1.
0
2.
C
3.
A
4.
B
Part B
1
a.
x2  x
binomial
2
20
b.
 x 2  x 1
trinomial
7
13
2
3
4
a. Binomial, 4
24 m  n , binomial
a. 6 x 2  3 y 2  4 y
5
a. x 2  9 x  2
6
 6 x 2  6 x, 36
7
8
3x  3
a.  8x 3 y 2 z
9
a.
10
4x 2 y
11
a.  2 x  4 x  5
12
a.
13
5x 2  x  4
4y2  y
14
4x
y3
2
3x 2
1
 2x 
2
2x
b. trinomial, 5
c. monomial, 0
b. 2 x 2  8 x  2
b. 5x 2  3x  6
b.  3s 5 t 4
b.
1
5a
c. 9y 2
b.
16 y 2  20 y
c.  6a  12a  6a
b. 3a 2  4a  5
3
2
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