Math 2 Unit 1
Day 4 – Polynomials review
Objectives
By the end of today, you will be able to…
• Classify polynomials
• Add, Subtract, and Multiply Polynomials
Vocabulary
• A polynomial is a monomial or the sum of monomials.
• The exponent of the variable in a term determines the degree of
that polynomial.
• Ordering the terms by descending order by degree. This order
demonstrates the standard form of a polynomial.
P(x) = 2x³ - 5x² - 2x + 5
Leading Cubic Term
Coefficient
Quadratic
Term
Linear Term
Constant
Term
Standard Form of a Polynomial
•For example: P(x) = 2x3 – 5x2 – 2x + 5
Polynomial
4x - 6x + 5
3x 3 + x 2 - 4x + 2x 3
6 - 2x 5
x 3 - 2x 2 - 3x 4
Standard Form
Polynomial
Parts of a Polynomial
P(x) = 2x3 – 5x2 – 2x + 5
•Leading Coefficient:
•Cubic Term:
•Quadratic Term:
•Linear Term:
•Constant Term:
Parts of a Polynomial
P(x) = 4x2 + 9x3 + 5 – 3x
•Leading Coefficient:
•Cubic Term:
•Quadratic Term:
•Linear Term:
•Constant Tem:
Classifying Polynomials
We can classify polynomials in two ways:
1) By the number of terms
# of Terms
Name
Example
1
Monomial
3x
2
Binomials
2x2 + 5
3
Trinomial
2x3 + 3x + 4
4
Polynomial with 4
terms
2x3 – 4x2 + 5x + 4
Classifying Polynomials
2) By the degree of the polynomial (or the largest
degree of any term of the polynomial.
Degree
Name
Example
0
Constant
7
1
Linear
2x + 5
2
Quadratic
2x2
3
Cubic
2x3 – 4x2 + 5x + 4
4
Quartic
x4 + 3x2
5
Quintic
3x5 – 3x + 7
Classifying Polynomials
Write each polynomial in standard form. Then classify it
by degree AND number of terms.
1. -7x2 + 8x5
2. x2 + 4x + 4x3 + 4
3. 4x + 3x + x2 + 5
4. 5 – 3x
Activity time!
Adding Polynomials
•
•
•
•
•
Add only like terms!
Organize the polynomials in the easiest way you can
see it; (vertically/horizontally).
Simplify all terms completely and totally.
Make sure of the signs in front of the parenthesis.
Cancel out any terms if necessary!
This is an example of how
to add polynomials and a good
way to group them to make
sure of the signs and like terms!
:)
Subtracting Polynomials
•
•
•
•
Set the problem up however you are comfortable;
(vertically or horizontally).
Remember to completely simplify the polynomials.
Pay attention to the sign infront of the parenthesis and
make sure to distribute it to all variables.
Cancel and simplify all variables and terms in the
polynomials.
This is an example of
subtracting
horizontally! Notice
the distribution of the
sign to the variables!
Multiplying Polynomials
• Choose to set up either the polynomials horizontally or
vertically; (based on preference).
• Keep in mind the signs in front of the variables.
• When multiplying the variables that contain an
•
exponent, instead of multiplying them together add
them instead.
Always distribute any number, sign, or variable in front
of parenthesis.
This demonstrates the principle of
distributing the terms in front of the
parenthesis and making sure of the
exponents.
CW & HW
• On your own sheet of paper, complete the
odd numbers for class work and turn them in.
• They will be assessed for both completeness
and accuracy so do your best!
• Finish the remainder of the worksheet for HW.