Warm UP
Factor out the Greatest common factor
1.
6n 2 – 12n
2.
2x 2 – 14x

Essential Question:
 What is a quadratic? How can I factor a quadratic?

Standard:
 MGSE9-12.A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
MGSE9-12.A.SSE.3a Factor any quadratic expression to reveal the zeros of the function defined by the expression

Standard Form
The standard form of any quadratic trinomial is ax 2  bx  c
So, in 3 x
2 
4 x

1 ...
a =3 b =-4 c= 1

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
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Now you try.
 x 2  7 x  2 a = b = c =
2 x 2  x  5 a =
4 x 2  x  2 a = b = b = c = c =

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Factoring when a =1 and c > 0.
x 2  8 x  12

First list all the factor pairs of c .
1 , 12
2 , 6
3 , 4

Then find the factors with a sum of b

These numbers are used to make the factored expression.
 x  2
  x  6

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Now you try.
x 2  8 x  15
Factors of c: x 2  10 x  21
Factors of c:

Circle the factors of c with the sum of b
Binomial Factors
( ) ( )
Circle the factors of c with the sum of b
Binomial Factors
( ) ( )

Factoring when c >0 and b < 0.
 c is positive and b is negative.
 Since a negative number times a negative number produces a positive answer, we can use the same method as before but…
 The binomial factors will have subtraction instead of addition.

x 2  13 x  12
First list the factors of 12 1 12
2 6
3 4
Make sure both values are negative!
 x  12
  x  1

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
Now you try.
1.
x 2  7 x  12
2.
x 2  9 x  14
3.
x 2  13 x  42
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Factoring when c < 0.
We still look for the factors of c .
However, in this case, one factor should be positive and the other negative in order to get a negative value for c
Remember that the only way we can multiply two numbers and come up with a negative answer, is if one is number is positive and the other is negative!

x 2  x 
In this case, one factor should be positive and the other negative.

We need a sum of -1
1 12
2 6
+
3
-
4
 x  3
  x  4

12


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Another Example x 2  3 x  18
List the factors of 18.
We need a sum of 3

What factors and signs will we use?
 x  3
  x  6

1 18
2 9
3 6

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1.
2.
3.
4.
x 2 x 2 x 2 x 2
 3 x  4
 x  20
 4 x  21
 10 x  56

Prime Trinomials
Sometimes you will find a quadratic trinomial that is not factorable.
You will know this when you cannot get b from the list of factors.
When you encounter this write not factorable prime .
or

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Here is an example… x 2  3 x  18 1 18
2 9
3 6
Since none of the pairs adds to 3, this trinomial is prime .

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
Now you try.
x 2  6 x  4 factorable prime x 2  10 x  39 factorable prime x 2  5 x  7 factorable prime
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Sometimes you can have a greatest common factor
2a 2 +10a – 12
 You have to factor out the Greatest common factor first

example
3v 2 + 36v + 81

Another example
6k 2 + 72 k + 192