Download 2.2 Adding, Subtracting and Multiplying Polynomials

4.2
Add, Subtract, Multiply
Polynomials
Objectives
•Define the terms/degree of a polynomial
•Simplify and evaluate by adding/subtracting/multiplying
•Evaluate polynomial function
PARTS OF A POLYNOMIAL
Terms of a polynomial are separated by +, −
Coefficients – numbers in front of variables
Constant – number without a variable
2
4𝑥 + 3𝑥 − 7
**Polynomials have non-negative integer exponents
CLASSIFY A POLYNOMIAL
Classify by terms:
Monomial (1 term): 2𝑥 2 ,
Binomial (2 terms): 𝑥 + 4,
7,
3𝑥𝑦,
8𝑦
2𝑥 4 − 3
Trinomial (3 terms): 3𝑥 2 − 2𝑥 + 7
*If more than 3 terms, it is a “polynomial with ___ terms” and no longer has a specific name.
CLASSIFY A POLYNOMIAL
Classify by degree:
The degree of a polynomial is the largest combined degree
of any single term.
ex: 2𝑦 − 7𝑥 2 𝑦 5 + 3𝑥𝑦
CLASSIFY A POLYNOMIAL
Identify the coefficient(s) and constant. Then classify the
polynomial by term(s) and degree.
1) 2𝑥 4
3) 2𝑚3 𝑛2 − 𝑚𝑛3 + 4𝑚𝑛2
2) 7𝑎3 − 4𝑎2 + 6𝑎 − 2
ADD/SUBTRACT POLYNOMIALS
To add (or subtract) polynomials, we combine the
coefficients of the like terms. The variables themselves and
exponents do not change.
ex:
14𝑥 2 + 3𝑥 − 7 + 2𝑥 + 5
= 14𝑥 2 + 5𝑥 − 2
ADD/SUBTRACT POLYNOMIALS
Combine the polynomials.
4) −5𝑥 3 + 6𝑥 2 + 2𝑥 − 7 + (3𝑥 3 + 4𝑥 + 1)
ADD/SUBTRACT POLYNOMIALS
Combine the polynomials.
5) 5𝑥 2 𝑦 − 3𝑥𝑦 + 12𝑥𝑦 2 + (𝑥 2 𝑦 + 12𝑥𝑦 − 5𝑥𝑦 2 )
ADD/SUBTRACT POLYNOMIALS
Combine the polynomials.
6) 6𝑧 3 + 2𝑧 2 − 5 − (−3𝑧 3 + 9𝑧 2 − 𝑧 + 1)
MULTIPLY POLYNOMIALS
Polynomials are multiplied using distribution.
To multiply terms, multiply the coefficients and add the
exponents using power rules.
7) 2𝑥 2 (𝑥 2 + 3𝑥 + 5)
MULTIPLY POLYNOMIALS
8) (2𝑦 − 3)(5𝑦 + 6)
9) 𝑥 + 6
2
MULTIPLY POLYNOMIALS
10) (2𝑥 + 5)(2𝑥 − 5)
11) (2𝑥 + 3)(𝑥 2 + 5𝑥 − 1)
POLYNOMIAL FUNCTION NOTATION
Let 𝑓 𝑥 = 3𝑥 2 and 𝑔 𝑥 = 𝑥 2 − 2𝑥 + 1
12
a) 𝑓 + 𝑔 𝑥 =
b) 𝑓 − 𝑔 4 =
POLYNOMIAL FUNCTION NOTATION
Let 𝑓 𝑥 = 3𝑥 2 and 𝑔 𝑥 = 𝑥 2 − 2𝑥 + 1
13
a) 𝑓 ⋅ 𝑔 𝑥 =
b) 𝑓 ⋅ 𝑔 −2 =