Concepts 1.1

1
Factoring Polynomials
5/24/2016
Factoring
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.
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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
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
11
Ticket Out the Door
Complete the Ticket Out the Door without
talking!!!!!
Talking time after the bell!
Put your NAME on the paper.
When finished, turn your paper face DOWN.
Factor.
12
Todays Homework
Rules for Homework

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

13
Homework
Factor.