Concepts 1.1

1
Polynomial Factoring
5/7/2016
Factoring, Difference of Two Squares
Objective factor a quadratic expression where
the a term does not equal one.
Students apply basic factoring techniques to
second-and simple third-degree polynomials. These
techniques include finding a common factor for
all terms in a polynomial, recognizing the
difference of two squares, and recognizing
perfect squares of binomials.
2
Notes

• Magic X

Ex.
Ex.
Ex.
Ex.
Ex.
Ex.
3
Notes

• Steps for Factoring a Quadratic Equation

1) Factor out the GCF (if possible)
2) Set up the Magic X.

• ac goes on top, and b goes on bottom

• Find the pair that multiplies to equal the top,
  and adds up to equal the bottom.

3) Set up the Magic T.

• Put ax on the top two, and the pair we found for
  the bottom two.

• Treat each side as a fraction and reduce if
  possible

4) You now have your factors.
4
Notes
Factor.
Ex.
1) Factor out GCF.
2) Magic X.
- What pair multiplies to equal top and adds to
equal the bottom?
3) Magic T.
- Reduce?
4) You now have your factors.
5
Notes
Factor.
Ex.
1) Factor out GCF.
2) Magic X.
- What pair multiplies to equal top and adds to
equal the bottom?
3) Magic T.
- Reduce?
4) You now have your factors.
6
Notes
Now you try.
Factor.
Ex.
1) Factor out GCF.
2) Magic X.
- What pair multiplies to equal top and adds to
equal the bottom?
3) Magic T.
- Reduce?
4) You now have your factors.
7
Notes
Factor.
Ex.
1) Factor out GCF.
2) Magic X.
- What pair multiplies to equal top and adds to
equal the bottom?
3) Magic T.
- Reduce?
4) You now have your factors.
8
Notes
Factor.
Ex.
1) Factor out GCF.
2) Magic X.
- What pair multiplies to equal top and adds to
equal the bottom?
3) Magic T.
- Reduce?
4) You now have your factors.
9
Notes
Now you try.
Factor.
Ex.
1) Factor out GCF.
2) Magic X.
- What pair multiplies to equal top and adds to
equal the bottom?
3) Magic T.
- Reduce?
4) You now have your factors.
10
Notes

• Difference of Two Squares

1. Must be subtraction.
2. Both terms must be perfect squares.
Determine if it the problem is a difference of
two squares.
Ex.
Ex.
Ex.
Now you try.
Ex.
Ex.
Ex.
11
Notes
Factor.
Ex.
Ex.
Ex.
Now you try.
Ex.
Ex.
Ex.
12
Summary
To factor a quadratic first set up the Magic
__. On top multiply ac and on _______ put b. Now
find a pair of numbers that ________ to equal the
top and ____ to equal the bottom. Next set up
your ______ T. Put ax on the top and put your
pair on the bottom. Reduce if possible.
X
bottom
multiply
Magic
add
You have a difference of ____ squares if both
terms are _______ squares and it is a __________
expression. If so, just break up each term and
make one parenthesis ________ and the other
subtraction.
two
subtraction
perfect
addition
13
Class Work / Homework
Rules for Homework

• Pencil ONLY.
• Must show all of your work.
• NO WORK NO CREDIT
• Must attempt EVERY problem.
• Always check your answers.

14
Class Work / Homework
Factor.