Chapter 7
Polynomial Equations and Factoring
7.1
Adding and Subtracting Polynomials
1. Students will be able to find the degree of monomials.
2. Students will be able to classify polynomials.
3. Students will be able to add and subtract polynomials.
Monomial – is a number, a variable, or the product of a number and
one or more variables with whole number exponents.
Degree of a Monomial – is the sum of the exponents of the variables
in the monomial. The degree of a nonzero constant term is 0. The
constant 0 does not have a degree.
Degree of a Monomial – is the sum of the exponents of the variables
in the monomial. The degree of a nonzero constant term is 0. The
constant 0 does not have a degree.
Monomial
Degree
Not a
monomial
Reason
10
0
A sum is not a monomial
3x
1
5+x
2
a
1 2
ab
2
1.8m5
1 2  3
4
a
x 1
5
A monomial cannot have a
variable in the denominator.
A monomial cannot have a
variable exponent.
The variable must have a
whole number exponent.
Find the degree of each monomial.
5x
2
2
1 3
 xy
2
4=1+3
8x 3 y 3
6=3+3
3
0
Polynomial – is a monomial or a sum of monomials. Each
monomial is called a term of the polynomial. A polynomial with two
terms is a Binomial. A polynomial with three terms is Trinomial.
Binomial
Trinomial
5x  2
x  5x  2
2
Degree of a Polynomial – is the greatest degree of its terms.
Standard Form – is when the exponents of the terms of a
polynomial decrease from left to right.
Leading Coefficient – is the coefficient of the first term when
you write a polynomial in standard form.
Standard Form – is when the exponents of the terms of a
polynomial decrease from left to right.
Leading Coefficient – is the coefficient of the first term when
you write a polynomial in standard form.
Degree of a Polynomial – is the greatest degree of its terms.
Leading
coefficient
Degree
2 x  x  5 x  12
3
2
Constant
Term
Write the polynomial in Standard Form, identify the degree, leading
coefficient and classify/name the polynomial.
15 x  x  3
4  9z
 x  15 x  3
9 z  4
3
3
Degree = 3
Degree = 1
Leading Coefficient = -1
Leading Coefficient = -9
Name = Trinomial
Name = Binomial
Write the polynomial in Standard Form, identify the degree, leading
coefficient and classify/name the polynomial.
4  5x  x
8q  q
5
3z
4
5x  x  4
q  8q
3z
4
2
2
5
Degree = 2
Degree = 5
Degree = 4
Leading Coefficient = 5
Leading Coefficient = 1
LC= -3
Name = Trinomial
Name = Binomial
Name = Monomial
Adding and Subtracting Polynomials – Combine like terms
Like terms – have the same variable and the same exponent
To Combine – just add or subtract the coefficients
(2 x  5 x  x)  (2 x  x  1)
3
2
2
Vertical Format
2 x  5x  x
3
2
 x  2x
3
2
1
3x  3x  x  1
3
2
3
(2 x  5 x  x)  (2 x  x  1)
3
2
2
3
Horizontal Format
(2 x  5 x  x)  ( 2 x  x  1)
3
2
2
3
(2 x  x )  (5 x  2 x )  ( x)  (1)
3
3
2
2
3x  3x  x  1
3
2
(3 x  x  6)  ( x  4 x  10)
2
Vertical Format
2
Horizontal Format
3x  x  6
(3 x  x  6)  ( x  4 x  10)
 x  4 x  10
(3 x  x )  ( x  4 x)  (6  10)
2
2
4x  5x  4
2
2
2
2
2
4x  5x  4
2
(4 x  5)  (2 x  2 x  4)
2
2
Vertical Format
4x
2
5
(2 x  2 x  4)
2
4x
2
5
 2x  2x  4
2
6x  2x  9
2
(4 x  3 x  5)  (3 x  x  8)
2
2
Horizontal Format
(4 x  3 x  5)  (3 x  x  8)
2
2
4 x  3x  5  3x  x  8
2
2
(4 x  3 x )  (3 x  x)  (5  8)
2
2
x  2 x  13
2
You Trys
( x  x  3)  (4 x  x  3)
2
2
x  x  3  4x  x  3
2
2
5x  2 x
2
( x  x  2)  (7 x  x)
2
2
x  x  2  7x  x
2
2
8x  2 x  2
2
Last One
YEH!!
But First
Let us review what we learned today
1. Students will be able to find the degree of monomials.
2. Students will be able to classify polynomials.
3. Students will be able to add and subtract polynomials.
And NOW…
( x  5)  (3 x  6)
2
 x  5  3x  6
2
3 x  x  11 Good Job!
2