Name ____________
Polynomials
A monomial is _______________________________
A polynomial is _______________________________
These are monomials
4x3 -7ab
1
y
These are NOT monomials
x
1
X2
1 5
y
2
-8
x2 + 4
2x2y
n2 + 2n + 5
Circle the polynomials:
X
-x2
½
0.024
5/x
x-2
2x+3y –4
8
A polynomial with 2 terms is a ____________________________
A polynomial with 3 terms is a ____________________________
A polynomial with more than 3 terms is a _____________________
Label each as M – monomial, B – binomial, T – trinomial, P – polynomial or
X if it is not a polynomial:
7
+ 4x – 1
x
___ 5n + 3
___ 3x2 + 2x – 4
___ 7
___ 5
___ 9 – 25x2
___ 3x + 3y + 3z
___ 2x + y – z + 4
___ m – 2m2
___ m 3
___ m2
___ 2x
___ x + 4x2 + 2x3
___
___ 3 + 21 – 4x + 5
___ 2a – b + 3c – d + 4e
___
1
st
2
2
5
m
___ x – 2y + z - 2n
___ 3.152x
The coefficient is _____________________________________
Identify the coefficient of each variable:
3x
___
-2x ___
3x
4
___
257m ___
 7x
6
___
4x + 7 ___
12  m
___
3
7n3
___
42 – n ___
3x2 ___
7 – x2 ___
x + 7 ____
3
- x + 4 ____
5
5 – 3 x ___
x + 2 ___
7
x – 5 ____
2
2x + 8 ____
5
x4
___
-x5
n
5
___
___
The degree of a monomial is ________________________________
Find the degree of each monomial:
6n2
___
13x7y3 ___
k4m2n5 ___
3m5n4 ___
8a4b ___
24
___
-r3s6t ___
7xy
___
2x4y ___
5x
___
-15
___
mn
___
5x7y3 ___
8
____
x2y
5
____
7x2y3z ___
-x5y7 ___
x
xy9
____
a6b3c4d2 ___
____
The degree of a polynomial is __________________________
Find the degree of each polynomial:
4x6y3 - 2xy5 + 5xy
___
___ ___
3x3y5z2 + 2x2y2z2 – x4y3z
___
___
___
9x4y – 2x3y – x2y4
___
___ ___
5xy5 - 2x3y2 + 4x4y5 - 9x2y2
___
___
___
___
2xy2 + 5x2y3 + 3xy
___
___ ___
9x4y6z2 + 6x7y5z + 4x5y6z3 + 3x8yz2
___
___
___ ___
6x2y – 3x4y – x3y4
___
___ ___
8xy5 - 4x3y2 + 9x2y2 - 2x2y5
___
___
___
___
3xy7 + 4x4y3 + 8xy
___
___ ___
2x5y7z2 + 7x8y5z + 3x4y8z3 + 3x9yz2
___
___
___ ___
7x8y – 3x6y – x3y5
___
___ ___
7xy2 - 6x2y2 + 5x4y - 4x2y2
___
___
___ ___
2xy6 + 3x5y3 + 4x4y5
___
___ ___
2x3y7z2 + 9x5y7z + 3x3y6z5 + 8x7yz3
___
___
___
__
Writing Polynomials
in
or
order
2x4y3 – 5x3y4 + 5x2 – x + 3
is written in descending order for the x variable. The term
with the greatest exponent for x is written first.
5 – 3xy3 + 4x3y4 – 3x5y3
is written in ascending order for the x variable. The term with
the lowest exponent for the x is written first.
What is the exponent for x in the term 5? _______
Arrange each polynomial in descending order for the x variable:
4x4 + 4x7 + x2 + 2x3 ___________________________________
3y + 4x5y2 – 4x2 + 5xy4 + 3x3 _____________________________
x + 3x5 + 4x3 + 5x2 + 6x7 – 2x4 ____________________________
- 14y + 7x2y3 – 10x3y2 – 14x7 ______________________________
Insert the term in the correct place for descending order according to the x:
3x4
5x5 + 2x3 + 7x + 1
2x
x3 + 3x2 + 5
X3y7
x5 y + x4y + x2y3
x2y4
x3y2 + xy5 + xy
2x3
x4 + 5x2 + 9x
9x2
3x5 + 4x4 + 7
Like Terms are ________________________________________________
Find 3 like terms in each row.
1.
6x
3y
x3
x
3
x
2.
8m2
-m
8mn
8
m
3.
5xy
4yz
3zy
2yz
z
4.
6ab
7ac
8bc
9ab
10ba
5.
6x2
3x3
4x3
5x
x3
6.
x2y
xy2
2x2y2
3x2y
5yx2
7.
3x
3w
x3
x
3
x
8.
4bvm
5mvb
6vmb
7mv
8mb
9.
7x
8x
9x
10x
x4
4
10.
4x2y3z
4
3
3xy2z3
4
8x3y2z
5x2y3z
6zx2y3
Combining Polynomials
1.
(x + 4) + (x – 3)
(x - 5) – (2x + 4)
_____________
_____________
_____________
_____________
3. (x2+ 5) – (2x –3)
4.
(5x2 –2x + 5) + (3x –7 + 2x2)
__________________
___________________
__________________
____________________
5. (x2 + 5) + (2 – 3x + 4x2)
7.
2.
6.
(5x3 – 8x2 + 1) – (4x + 5 – x3 + 2x2)
___________________
_____________________________
___________________
______________________________
(7x - 8) + (4x – 3)
8.
(8 - x) – (x + 4)
__________________
_____________________
__________________
______________________
9. (6x2+ 2x ) – (2x – 3)
10.
(3x2 + 7x - 5) + (3x – 7 + 5x2)
__________________
_______________________
__________________
_______________________
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Polynomials