Name ___________________________
Date ____________
Unit 10 - Polynomials
Aim #82: Adding and Subtracting Polynomials
Do Now
1) How many terms does 8x2 +10x + 9 have?
2) Simplify using the distributive property.
a) -5(x +3)
3) State the additive inverse of each term.
a) 9
b) -8y2
b) 7x -(2x - 4)
c) 3x
Polynomials
A polynomial is an expression consisting of the sum of one or more terms.
Type of Expression
Definition
Monomial
(mono means ________)
Polynomial with ______ term
Binomial
(bi means ________)
Polynomial with _______
terms
Trinomial
(tri means _______)
Polynomial with __________
terms
Polynomial
(poly means ________)
Expression with one or
________ terms
Example
Standard form: arranging the terms so that the exponents decrease from left to right
Ex: 5x2 +3x4 +1-7x -9x3
Adding Polynomials
Ex #1: (4x2 +8x -2) +(3x2 -5x + 7)
Step 1: Combine like terms
Ex #2:
(7n2 +15n -13) +(4n2 +2)
Subtracting Polynomials
Ex #3: (5x2 +3x -1) -(2x2 - 4x + 9)
Step 1:Take the additive
inverse of the
second polynomial
Step 2: Combine like terms
Ex #4: Subtract -3xy +10x -2y from 7xy - y -8x
Classify each polynomial by its number of terms.
1)
5y - 9 ___________________
2)
15x2 + 8x - 3 ___________________
3)
4x2y ___________________
4)
12a3 - 8a2 + 2a - 1 ___________________
5)
10x3y2 - 7x2y3 __________________ 6)
7 ___________________
Write each polynomial in standard form.
7) 9y2 - 10 + 3y + 10y3 _________________ 8) 3a - 5a4 + 6a2 - a3 + 1 _________________
Add or subtract.
9)
(x2 + 3x + 5) + (2x2 - 4x - 1)
10)
(5x2 + 3y) + (9x + 6y)
11)
(8x2 + 4x - 2) - (3x3 – x2 + 5)
12)
(8x – 5xy) - (3xy + 2x)
13)
(3y2 - 2y - 1) - (-5y2 + 2y + 6)
14)
(x3 - 23x2 + 10x) + (-7x3 + 3x2 – 10x)
15)
(-6a + b) + (-5a - 4b + c)
16)
(9n2 + 5n - 4) - (5 + n2)
17)
(x4 + 5x2 - 24) + (-x4 - 4x2 + 9)
18)
(2x + 3y + 4) - (5x - y - 12)
19)
(-6x2 + 4x) + (-3x2 + 7x + 8)
20)
(14x3 + 3x - 2) - (-3x2 - 7x + 1)
21)
(8y2 + 3y - 6) - (3y2 - 5y)
22)
(20x2 + 5x - 3) - (2x2 - 3x - 4)
23)
(-2x2 + 7x - 15) - (4x2 - x - 5)
24)
(2y2 + y + 18) + (3y2 - 7y - 2)
25)
(12xy – 4x + y) - (2y + 14xy – 5x)
26) Subtract 7x2 + 3x - 8 from 9x2 - 3x - 7.