Download Add Subtract and Multiply Polynomials

1. What are the Properties of
Exponents?
 2. How do we convert between
exponential and radical form?
 3. How do we add, subtract, and
multiply polynomials?

Properties of Exponents &
Performing Operations with Polynomials
(Adding, Subtracting, & Multiplying)



What are
Polynomials?



Mono- is a prefix
meaning “one”
Bi- is a prefix
meaning “two”
Tri- is a prefix
meaning “three”
Poly- is a prefix
meaning “many”
-nomial is a suffix
meaning “terms”
Polynomial = Many
Terms

How do we work
with

Polynomials?

We can perform operations
with polynomials (addition,
subtraction, multiplication,
and division). (Division is
taught in Math III).
When we write polynomials,
the standard is to write in
descending order of the
exponents.
The degree of a polynomial
is the highest exponent or
sum of the exponents if there
are multiple variables in the
same term.




1.
2.
3.
4.
5p2 – 3
a3 – 2a2
3 – 6n5 – 8n4
-10x4y3 + 6y3 + 4x4y4




A. trinomial degree 8
B. binomial degree 2
C. trinomial degree 5
D. binomial degree 3
Combining Like Terms
Adding the Opposite.
ADDING POLYNOMIALS




(5p2 -3) + (2p2 – 3p3)
Identify like terms and
combine them.
5p2 + 2p2 = 7p2
Write in descending
order of the exponents.
-3p3 + 7p2 -3
SUBTRACTING POLYNOMIALS




(a3 – 2a2) – (3a2 – 4a3)
Add the opposite, so…
(a3 – 2a2) + (-3a2 + 4a3)
Combine like terms…
a3 + 4a3 = 5a3
-2a2 + -3a2 = -5a2
5a3 – 5a2





(-7x5 + 14 – 2x) + (10x4 + 7x + 5x5)
Reorder
-7x5 + 5x5 +10x4 – 2x + 7x + 14
Combine like terms
-2x5 + 10x4 + 5x + 14





(8n – 3n4 + 10n2) – (3n2 + 11n4 – 7)
8n – 3n4 + 10n2 + -3n2 + -11n4 + 7
-3n4 + -11n4 + 10n2 + -3n2 + 8n + 7
Combine like terms
-14n4 + 7n2 + 8n + 7
When multiplying, multiply the
constants, then the variables.
 Remember to use the laws of
exponents (when multiplying you
add the exponents).
 Ex:
2x2 * 5x3 = 10x5

 To
multiply a monomial and
a polynomial, you simply
distribute.
 Ex:
2x2 (3x3 – 4x2 + x – 5)
6x5 – 8x4 + 2x3 – 10x2





FOIL – multiply first, outside, inside,
then last (basically distribute)
Box it – draw a box, put the numbers
in, multiply and combine like terms.
Examples:
1. (x + 2) (x + 5)
2. (3x + 10) (2x – 5)


1) Distribute 2) Line up your like terms 3)
Add
Or… Box it
Ex:
1. (x + 2) (x2 + 5x + 6)
2. (x2 – 2x + 1) (x2 + 5x + 6)
3. (2x2 – 3x + 4) (x4 + 2x3 – 4x – 3)
On Notebook Paper:
 Classwork: Odd Problems
 Homework: Even Problems





1. When do you add the exponents?
2. When do you subtract the exponents?
3. When do you multiply the exponents?
4. How do you get 1 when using
exponents?
5. If something is raised to the 1/3
power, what is the root?