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FACTORING QUADRATICS

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by

Ann Weir

on 23 July 2014

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Transcript of FACTORING QUADRATICS

FACTORING
QUADRATICS

GCM
Always start by checking if there's a common monomial that can be factored out of each term. If there is use the distributive property to factor it out.
Example
Example
Example
Example
Note the original expression is not quadratic, but this is still an example of factoring out a GCM.
Video
Note: GCF is the same as GCM
When
a
=1

Set up your parentheses
Find two number that add to b and
multiply to c.
Example
Determining Whether the Parentheses
are Addition or Subtraction when a = 1
and the Quadratic is Factorable
If
b
and
c
are both positive the operations in the parentheses
will both be addition.
If
b
is negative
c
is positive the operations in the parentheses
will both be subtraction.
If
b
and
c
are both negative one of the operations in the parentheses will be one addition and one subtraction.
If
b
is positive
c
is negative the operations in the parentheses
will be one addition and one subtraction.
If
b
is zero and
c
is negative the operations in the parentheses will be one addition and one subtraction.
If
b
is zero and
c
is positive the quadratic can not be factored.
Remember Not All Quadratics
Can Be Factored!
There are no values m and n that will multiply to 25 and also add to zero.
Even if
b
is not zero the quadratic may not be able to be factored.
There are no values m and n that will multiply to -7 and also add to 5.
Example
Can't be factored because there aren't two numbers that multiply to 36 and add to 0.
Example
Example
Example
Example
Example
Can't be factored because there aren't two numbers that multiply to -26 and add to 15.
Video
When
a
does not equal 1

Guess and check. Pick two numbers that multiply to
a
and two numbers that multiply to
c
. Then check the inner and outer to make sure that the middle terms add to
b.
If they don't add to
b
you will need to keep trying other combinations that multiply to
a
and
c.
Look at
a
and
c
and if one of them has less factors than the other start with it first.
While guessing and checking keep in mind that if there was no GCM the factors will not have a GCM. Knowing this can reduce the number of combinations you need to try.
If there's no GCM and
b
is zero and
a
and
c
are positive the quadratic can not be factored.
Remember Not All Quadratics
Can Be Factored!
Think of the graph. It is concave up and the vertex is at (0,5).
If you've tried every possible combination and none of them work the quadratic can't be factored.
The factors of 3 are 3 and 1 and the factors of 5 would be -1 and -5, but there's no combination of these that would give you an inner and outer sum of -1x.
Hints:
Hints:
Two only has the factors 2 and 1 so start by putting 2x and x in the parentheses.
Now test numbers that multiply to -6 and make sure you check the inner and outer.
The inner is -1x and the outer is -5x which is a sum of -16x.
The inner is -5x and the outer is -3x which is a sum of -8x.
If there's no GCM and
b
is zero and
a
and
c
are negative the quadratic can not be factored.
Think of the graph. It is concave down and the vertex is at (0,-3).
If you wanted to try 2 and 5 next you'd know that the 2 can't go in the parentheses that already have a 2. If it could that would mean the original quadratic had a GCM of 2 as well.
Example
Example
Example
Example
Video
Make sure you have the volume on!
Full transcript