1. Today:
1. Warm-Up
2. New Khan Academy Topics
3. Factoring Polynomials
4. Special Products
5. Class Work
3/18/15

2. 1. 5(4x - 4) - 3 = 37
2
4. A 20% profit was made on an item selling for $60. What
was the cost of the item?
2. FACTOR: 3xy - 21y + 5x – 35
3. FACTOR: 6mx – 4m + 3rx – 2r
Warm-Up:

3. Linear vs. Quadratic Equations
1. Write a Linear Equation, any linear equation
2. Write the Linear Equation in both standard and
slope-intercept form.
Fill in the blank: (In your notebook)
3. The highest degree of any linear equation is _______.
The angle of the line depends on the _______, and every
linear equation results in a ________ line.
1
slope
straight
4. Write the equation of
the given line
Warm-Up:

4. Khan Academy Topics for this week:
Thursday: Factoring Quadratics 2
Class Notes Section of Notebook, please

5. Polynomials
Factoring
Today:
1. Review
2. Factor x2
+ bx + c Trinomials
3. Special Products
Class Notes Section of Notebook

6. Instead of simply memorizing rules & formulas, it really2
helps
to understand why (for what purpose), you are adding,
subtracting, factoring, etc.
Remember, terms are separated by + or – signs. (The terms are
all being added or subtracted). An example is: 10x2
+ 15x
Factoring is finding an equal expression that is a product, that
is, the factors are multiplied. How do we factor 10x2
+ 15x ???
The first step is to always look for a common factor. Is there one
for this polynomial?We factor out the GCF of 5x. What remains
is (2x + 3). The full factor is 5x(2x + 3).
10x2
+ 15x = 5x(2x + 3)
We multiply factors to find the terms of a polynomial.
(These terms are either being added or subtracted.)
The Main Idea

7. Steps to Factoring Completely:
1. Look for the GCF
2. Look for special cases.
a. difference of two
squares,
b. perfect square
trinomial
3. If a trinomial is not a perfect
square, look for two different
binomial factors.
coming soon..
4. If a polynomial has 4 terms,
you can try to factor by grouping.
6. Not all polynomials can be
factored.
...today
5. Understand what you are
working with before you attempt
to factor.
...yesterday

8. To solve these, we use FOIL in reverse.
x2 + x – 6 = (x ) ( x )
Check the signs:
Then, list all the factors of the last term, looking for the
sum of the middle term, and the product of the last term.
Factoring Trinomials: (1x2 + bx + c)
(The leading coefficient is always 1)
x2 + x – 6 =
x2 + x – 6 =6
1,6
2,3
(x + )(x - )
(x + 3)(x - 2 )
No algebra magic or wizardry here.
Factor and check for the correct fit.
 When trinomials have a degree of “2”, they are known as quadratics.

9. FOIL With a Positive and a Negative
(x + 3)(x - 5)
F = (x•x) = x2
O = (x•-5) -5x
I = (3•x) +3x
L = (3•-5) -15
Answer: x2 - 2x - 15
The larger number is negative,
so the middle term is negative.

10. (x - 3)(x + 5)
FOIL With a Negative and a Positive
The opposite of our first example. The
larger number is positive, resulting in a
positive middle term.
Answer: x2 + 2x - 15
...But I thought if the signs were different, the middle
term was cancelled out?
This is true, but only if the two numbers are the same!
(3x + 5)(3x – 5)

11. Factor the polynomial x2 + 13x + 30. That was too easy,
one more
Factor the polynomial x2 – 2x – 35.
Since our two numbers must have a product of – 35 and a sum of
– 2, the two numbers will have to have different signs.
Factors of – 35 Sum of Factors
– 1, 35 34
1, – 35 – 34
– 5, 7 2
5, – 7 – 2
Factor: 2ab2 – 26ab – 60a

12. Square of a sum
Square of a difference
Difference of Squares
Special Products
**Be able to recognize them in both factored and expanded form

13. Products...Special
9x2 - 16x2
Factor:
18y3 – 8y
4m2 – 49n2 =
(2m)2 – (7n)2 Difference of
squares
(2m + 7n)(2m – 7m)
What type of special
product are these?
difference of squares:
Find each Product (Expand), or Factor:

14. Class Work 3.9
 Ample class time was left for you to work on 3.9 as there
are more than the average number of problems to complete
Friday is the absolute latest this class work will be accepted
for credit.
Some problems will require more than one factoring
As mentioned earlier, be aware of difference of squares and
the other two special products.