**FACTORING**

QUADRATICS

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

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

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!