3.1 - Adding and
Subtracting Polynomials
How do we identify,
evaluate, add, and
subtract polynomials?
What is a polynomial?
The prefix ‘Poly’ means
many. The root word, or
nomial, refers to a term(s).
What are some specific
types of Polynomials?
(According to the number of terms!)
Monomial
One Term
Binomial
Two Terms
Trinomial
Three Terms
What do we mean when
we ask for the Degree of
the Polynomial?
The degree of the polynomial
is given by the term with the
largest exponential value.
Example 1:
In this example, the degree of
the polynomial is 5, and the
leading coefficient is 2.
Classifying Polynomials by
Degree
Degree of 0
Constant - No Variables Visible
Degree of 1
Linear
- y = mx + b
Degree of 2
Quadratic
- Parabola
Degree of 3
Cubic
Degree of 4
Quartic
Degree of 5
Quintic
Example 2:
Rewrite in standard form. Then, identify the
leading coefficient, degree, and number of terms.
Name the polynomial.
Leading coefficient:
1
Degree of Polynomial: 3
Number of Terms:
4 terms
Name of Polynomial:
Cubic
Example 3:
Rewrite in standard form. Then, identify the
leading coefficient, degree, and number of terms.
Name the polynomial.
Leading coefficient:
-4
Degree of Polynomial: 3
Number of Terms:
2 terms
Name of Polynomial:
Cubic
- binomial
Example 4:
Rewrite in standard form. Then, identify the
leading coefficient, degree, and number of terms.
Name the polynomial.
Leading coefficient:
4
Degree of Polynomial: 4
Number of Terms:
4 terms
Name of Polynomial:
Quartic
How do we add
polynomials?
●
●
To add polynomials, we
combine the “like” terms.
To do this, we add the
coefficients of “like” terms
only...NOT exponents!
Example 5:
Add the following. Be sure to write your answer
in standard form.
Example 6:
Add the following. Be sure to write your answer
in standard form.
How do we subtract
polynomials?
The subtraction sign in front of
the parenthesis changes the sign
of everything inside of the
parenthesis that follows.
(Then we can follow the rules of addition!)
Example 7:
Subtract the following. Be sure to write your
answer in standard form.
Example 8:
Your Turn:
Add or Subtract the following. Be sure to write
your answer in standard form.
Solutions:
Challenge Yourself!:
Add or Subtract the following. Be sure to write
your answer in standard form.
1)
2)
3)
Solutions:
1)
2)
3)