Download degree - tpratt3khs

Warm Up
Combine like terms:
6x – 2xy – 7z + 4 – 3y + x – 7xy + 3y + 8 - xz
What does each prefix mean?
mono
bi
tri
Polynomials
A monomial is the product of numbers,
variables, or both.
Ex. 5 x 6y 7jk2
A polynomial is a monomial or a group
of monomials separated by + or –.
Ex. 7x2 + 8xk - 4
State whether each expression is a
polynomial. If it is, identify it.
1) 7y - 3x + 4
2) 10x3yz2
5
 7y
3)
2
2y
The degree of a monomial is the sum
of the exponents of the variables.
Find the degree of each monomial.
1) 5x2
1) 4a4b3c
3) -3
To find the degree of a polynomial, use the
monomial with the highest degree.
1) 8x2 - 2x + 7
Degrees:
Which is biggest?
2) y7 + 6y4 + 3x4m4
Degrees:
Find the degree of
1.
2.
3.
4.
5.
0
2
3
5
10
5
x
–
3
2
xy
+4
Sometimes, a polynomial will already be
factored. When this is the case, add up all
the exponents.
Ex. (x-2)3(x+5)2(x-3)(x+7)(x+1)3
Quick Recap
To find the degree of a polynomial, use the monomial
with the largest degree.
7x3y + 9x2 + 4x + 5y
If the polynomial is already factored, add up the
exponents.
(x-3)(x+4)(x-7) 3
Naming Polynomials
By Degree
Degree
0
1
2
3
4
5
Name
Constant
Linear
Quadratic
Cubic
Quartic
Quintic
By Terms
Number of
Terms
1
2
3
4 or more
Name
Monomial
Binomial
Trinomial
“with 4
terms”
(or 5 or 6,
etc.)
Try it! Name the following polynomials:
• x3
• x5 – xy + 3y2
• t2 – 8
• j4 + 6jk – 3j + 2
Adding and Subtracting Polynomials
• Combine like terms.
• Watch out for degrees!
Don’t combine x and x2.
• When subtracting, be sure to distribute the
negative to all terms.
Example 1:
Add the following polynomials:
(9y - 7x + 15a) + (-3y + 8x - 8a)
Example 2:
Add the following polynomials:
(3a2 + 3ab - b2) + (4ab + 6b2)
Example 3:
Add the following polynomials:
(4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2)
Example 4:
Subtract the following polynomials:
(9y - 7x + 15a) - (-3y + 8x - 8a)
Example 5:
Subtract the following polynomials:
(7a - 10b) - (3a + 4b)
Example 6:
Subtract the following polynomials:
(4x2 - 2xy + 3y2) - (-3x2 - xy + 2y2)
Find the sum or difference.
(5a – 3b) + (2a + 6b)
1.
2.
3.
4.
3a – 9b
3a + 3b
7a + 3b
7a – 3b
Find the sum or difference.
(5a – 3b) – (2a + 6b)
1.
2.
3.
4.
3a – 9b
3a + 3b
7a + 3b
7a – 9b