Lesson
10.1
Adding and subtracting polynomials
Objective: To add and subtract polynomials
To classify polynomial by degree and by
number of terms
Example of a Polynomial
Degrees
4 x  6 x  3x  5
3
2
Constant
Coefficients
Vocabulary
Degree: is the exponent for each variable.
Degree of the polynomial: is the largest exponent of the
polynomial.
Leading coefficient: is the coefficient of the first term.
Descending order/Standard form is how polynomials are
written where the terms are placed in descending order
from largest degree to smallest.
Example: Write the polynomials in Standard form/descending order.
Then identify the leading coefficient and degree of the polynomial.
1.
5 x  3x  x
2
7
3
3x  x  5 x
7
3
2
Degree is 7
Leading coefficient is 3
2.
4x  2x 1
4
 2x  4x 1
4
Degree is 4
leading coefficient is –2
By Degree
Classifying Polynomials
Degree
Example
Example
Constant
0
6
-3
Linear
1
3x + 4
-7x + 2
Quadratic
2
3x 2  2 x  1
 6x2  4
Cubic
3
5x3  2 x 2  3
3x 3  x
4
4
2
5
x

8
x
x
3x  x  2
Quartic
4
3
Classifying polynomials
# of terms
By # of terms
Example
Example
Monomial
1
3x
7x2
Binomial
2
3x + 1
8x3  2 x
Trinomial
3
 3x 6  2 x 2  5
4 x 2  3x  5
Note: Any polynomials with four or more terms are just
called polynomials
Adding polynomials
Write answers in descending order
Combine like terms to add polynomials
EX:
EX:
(3x  4 x  6)  (2 x  7 x  1)
2
2
(4 x  5x  2)  (6 x  9)
3
2
2
 5 x  3x  5
2
 4 x  11x  7
3
2
Subtracting Polynomials
1.
(5x  3x  3)  (2 x  4 x  6)  3 x 2  7 x  9
2.
(5x  3x  8x)  (2 x  5)
2
6
2
3
3
 5x  x  8x  5
6
3