1. Adding and Subtracting Polynomials (9.1)
Objective:
Students will add and subtract polynomials.

2. Algebra Standards:
10.0 Students add, subtract, multiply and divide monomials
and polynomials. Students solve multi-step problems,
including word problems, using these techniques.

3. is a number, a variable, or the product of a number and one or more
Vocabulary
Monomial
is a number, a variable, or the
product of a number and one or more
variables with whole number
exponents. 8
-2x
-3x2y
½x2
Degree of a Monomial
is the sum of the exponents of the variables in
the monomial.
-2x
-3x2y 5
-3x5 1 3 5

4. Vocabulary
Polynomial
is a monomial or a sum of monomials
4x3
-2x + 2
7x2 – 4x + 6
Binomial:
two-term polynomial
x + 2
4x3 + 2x
-2x2 – 5
Trinomial:
three-term polynomial
x2 + 2x – 1
5x5 – 5x + 2
-x4 + 2x2 – 4x

5. Polynomial Degree Identified by Degree Identified by Number of Terms
#1 Identify Polynomials
Polynomial
Degree
Identified
by Degree
Identified by
Number of Terms
a) -3
constant
monomial 1
linear
binomial
b) –x + 1 2
quadratic
binomial
c) x2 + 3
d) 5x3 – 3x2 + x – 8 3
cubic
polynomial

6. b) (-3x3 + 11x2 – 8x + x5 + 2) + (8x – 2x4 + 7x3 – 3 + 12x2)
#2 Add Polynomials
a) (2x2 + x – 5) + (x + x )
2x2
+ x
– 5 x2
+ x
+ 6
3x2
+ 2x
+ 1
b) (-3x3 + 11x2 – 8x + x5 + 2) + (8x – 2x4 + 7x3 – x2) x5
+ 0x4
– 3x3
+ 11x2
– 8x
+ 2
0x5
– 2x4
+ 7x3
+ 12x2
+ 8x
– 3 x5
– 2x4
+ 4x3
+ 23x2
– 1

7. Check Point:
c) (2x6 – x5 + 3x3 – 14x2 +13) + (7x5 – x4 + 9x3 + 13x2+ 2)
2x6
– x5
+ 0x4
+ 3x3
– 14x2
+ 0x
+ 13
0x6
+ 7x5
– x4
+ 9x3
+ 13x2
+ 0x
+ 2
2x6
+ 6x5
– x4
+ 12x3
– x2
+ 15
2x6
+ 6x5
– x4
+ 12x3
– x2
+ 15

8. (-3x3 + 11x2 – 8x + x5 + 2) – (2x – 4x4 – 3x3 – 3 + 6x2)
#3 Subtract Polynomials
(11x4 + x3 – x + 5) – (-x4 – x2 + 2x + 8 )
11x4
+ x3
+ 0x2
– x
+ 5
+x4
+ 0x3
+ x2
– 2x
– 8
12x4
+ x3
+ x2
– 3x
– 3
(-3x3 + 11x2 – 8x + x5 + 2) – (2x – 4x4 – 3x3 – 3 + 6x2) x5
+ 0x4
– 3x3
+ 11x2
– 8x
+ 2
0x5
+ 4x4
+ 3x3
– 6x2
– 2x
+ 3 x5
+ 4x4
+ 5x2
– 10x2
+ 5

9. Check Point:
(3x5 + 7x3 – 13x2 – 10x + 9) – (x5 – 4x x2 – 2x – 7 )
3x5
+ 0x4
+ 7x3
– 13x2
– 10x
+ 9
-x5
+ 4x4
+ 0x3
– 11x2
+ 2x
+ 7
2x5
+ 4x4
+ 7x3
– 24x2
– 8x
+ 16
2x5
+ 4x4
+ 7x3
– 24x2
– 8x
+ 16

10. A B C
Find the length of in terms of x. 1) + = 2) =

11. Find the area of quadrilateral ABCD in
terms of x. A B + C D

12. A B C
Find the length of in terms of x. 1) = 2) =

13. Find the area of if the area of
rectangle LMNO is L M P O N

14. Assignment
Book Pg. 373
# 1 – 8 all
# 15 – 20 all
# 23, 24, 28, 36, 37, 45, 61, 66, 70