A.3a Polynomials
and Factoring
Only a life lived for others
is a life worthwhile.
-Albert Einstein
Definitions
Monomial: the product of a constant and a variable
raised to a nonnegative integer power.
ax
coefficient of the monomial
(constant value)
k
variable
degree of the
monomial (power
of the variable)

Definitions
Like terms: two monomials with the same degree and the
same variable
We know that we can add and subtract like terms
3x 2  4 y  2x  6  5x 2  3y 2  3x 1
Definitions
Binomial: the sum or difference of two monomials that are
not like terms
Trinomial: the sum or difference of three monomials that are
not like terms
Polynomial: the sum or difference of monomials that are
not like terms
Definitions
Terms: the monomials that make up a polynomial
Standard Form: polynomial written beginning with the
term of highest degree and continuing in descending order
3x  x  4 x  7
4

2
Special Products
Difference of two squares:
x 2  a2  (x  a)(x  a)
Ex: 4 x 2  25
Sumand Difference of Cubes:
x 3  a 3  (x  a)(x 2  ax  a 2 )

x 3  a 3  (x  a)(x 2  ax  a 2 )
Ex: 8x 3  1


These are important rules for factoring!
Factoring:
Ex: 4 x 2 10x  24
Factoring: Grouping
Ex. 3x 3  2x 2 12x  8
Factoring Practice
1. x 4  16
6
2
2. 72x  98x
3. 6x 2  11x  7
4. 20x 6 12x 5  35x 3  21x 2
5. 8x 3  32x 2  30x
6. 4 x 3  20 x 2  9 x  45
A.3a Polynomials
and Factoring
Homework:
Page 975
25-53 EOO
Only a life lived for others
is a life worthwhile.
-Albert Einstein