1. Quiz 5-3
1. Simplify:
2. Simplify:
Simplify (special pattern):

2. Section 5-4 Factor and solve Polynomial Equations

3. Vocabulary Prime Polynomial: A polynomial where
the coefficient of each term has no common
factor with any other coefficients and…
it cannot be factored into polynomials of
lesser degree.
(There is no number (other than +1 or -1)
that is common to all of these terms.)
This is important because if you can factor out the common term, it will end up being easier to factor the polynomial.

4. NOT a prime polynomial 3 is a common factor of each term
We can “factor out” the 3

5. Prime vs. Not Prime Polynomials:
Example: is prime because it cannot be factored.
Example: is not prime because it can be factored.

6. Your Turn: Are these prime polynomials or not? If not,
write it in factored form. 1. 2.

7. More Vocabulary Factored completely: a polynomial is
factored completely if it is written as the
product of a monomial and one or more
prime polynomials.
Example:
Can this be factored?

8. Your Turn:
3. Factor this polynomial completely

9. Move Vocabulary Factor by grouping: some polynomials can be
factored easily if they have pairs of terms that
have a common monomial factor.
What’s the
common monomial
factor here?
What’s the
common monomial
factor here?
Are both of these
factors prime?
Do these two expressions
have a common factor?

10. Hints on factoring by grouping
You need two pairs of terms in order to factor by grouping
If they give you a 4 term polynomial, try factoring by grouping.

11. Your turn:
(problems 2 and 3 in the green book)
4. Factor

12. Special Patterns (we learned these last time)
Sum of 2 “cubes”
Difference of 2 “cubes”
Difference of 2 “squares”

13. Your turn: Factor completely (special pattern) 5. 6.
(prob. #1 pg 143 green book) 5. 6.

14. What does solving a polynomial mean?
Where does the polynomial cross the x-axis.

15. Solve by factoring Solve  rewrite the equation so that it = 0
Factor the polynomial
Use the Zero product rule to find the solution.
How many times does this
polynomial cross the x-axis?
x = 3, -3, 1, -1

16. Your turn: 7. Solve the polynomial.
(problem #4 on green book page 143)