Factoring
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Factoring. Polynomials. Factoring a polynomial means expressing it as a product of other polynomials. Factoring Method #1. Factoring polynomials with a common monomial factor (using GCF). **Always look for a GCF before using any other factoring method. Steps:.

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Factoring

Factoring

Polynomials


Factoring

Factoring a polynomial means expressing it as a product of other polynomials.


Factoring

Factoring Method #1

Factoring polynomials with a common monomial factor (using GCF).

**Always look for a GCF before using any other factoring method.


Factoring

Steps:

1. Find the greatest common factor (GCF).

2. Divide the polynomial by the GCF. The quotient is the other factor.

3. Express the polynomial as the product of the quotient and the GCF.


Factoring

Step 1:

Step 2: Divide by GCF


Factoring

The answer should look like this:


Factoring

Factor these on your own looking for a GCF.


Factoring

Factoring Method #2

Factoring polynomials that are a difference of squares.


Factoring

A “Difference of Squares” is a binomial (*2 terms only*) and it factors like this:


Factoring

To factor, express each term as a square of a monomial then apply the rule...


Factoring

Here is another example:


Factoring

Try these on your own:


End of day 1

End of Day 1


Factoring

Sum and Difference of Cubes:


Factoring

Apply the rule for sum of cubes:

Write each monomial as a cube and apply either of the rules.

Rewrite as cubes


Factoring

Apply the rule for difference of cubes:

Rewrite as cubes


Factoring

Factoring a trinomial in the form:

where a = 1

Factoring Method #3


Factoring

Factoring a trinomial:

1. Write two sets of parenthesis, (x )(x). These will be the factors of the trinomial.

2. Find the factors of the c term that add to

the b term. For instance, let

c = d·eand d+e = b

then the factors are

(x+d)(x+e ).

.

Next


Factoring

x

x

-2

-4

1 + 8 = 9

2 + 4 = 6

-1 - 8 = -9

-2 - 4 = -6

Factors of +8: 1 & 8

2 & 4

-1 & -8

-2 & -4

Factors of +8 that add to -6


Factoring

F

O

I

L

Check your answer by using FOIL


Factoring

Lets do another example:

Don’t Forget Method #1.

Always check for GCF before you do anything else.

Find a GCF

Factor trinomial


Factoring

When a>1, let’s do something different!

Step 1:

Multiply a · c

= - 30

Step 2: Find the factors of a·c (-30) that add to the b term


Factoring

Factors of 6 · (-5) :1, -30 1+-30 = -29

-1, 30 -1+30 = 29

2, -15 2+-15 =-13

-2, 15 -2+15 =13

3, -10 3+ -10 =-7

-3, 10 -3+ 10 =7

5, -6 5+ -6 = -2

-5, 6 -5+6 =1

Step 2: Find the factors of a·c that add to the b term

Let a·c = d and d = e·f

then e+f = b

d = -30

e = -2

f = 15


Factoring

-2, 15 -2+15 =13

Step 3: Rewrite the expression separating

the b term using the factors e and f

-2x+15x -5

13x

Step 4: Group the first

two and last two terms.

-2x + 15x -5


Factoring

Step 4: Group the first

Two and last two terms.

Step 5: Factor GCF

from each group

Check!!!! If you cannot

find two common factors,

Then this method does

not work.

Step 6: Factor out GCF

- 2x + 15x - 5

3x - 1)+ 5(3x - 1)

Common factors

3x - 1)(2x + 5)


Factoring

I am not a

fan of guess

and check!

Try:

F

O

I

L

Step 3: Place the factors inside the parenthesis until O + I = bx.

This doesn’t work!!

O + I = 30 x - x = 29x


Factoring

F

O

I

L

Switch the order of the second terms

and try again.

This doesn’t work!!

O + I = -6x + 5x = -x


Factoring

F

O

I

L

O+I = 15x - 2x =13x

IT WORKS!!

Try another combination:

Switch to 3x and 2x


Factoring

Factoring Technique #3

continued

Factoring a perfect squaretrinomial in the form:


Factoring

Perfect Square Trinomials can be factored just like other trinomials (guess and check), but if you recognize the perfect squares pattern, follow the formula!


Factoring

b

a

Does the middle term fit the pattern, 2ab?

Yes, the factors are (a + b)2 :


Factoring

b

a

Does the middle term fit the pattern, 2ab?

Yes, the factors are (a - b)2 :


Factoring

Factoring Technique #4

Factoring By Grouping

for polynomials

with 4 or more terms


Factoring

1. Group the first set of terms and last set of terms with parentheses.

2. Factor out the GCF from each group so that both sets of parentheses contain the same factors.

3. Factor out the GCF again (the GCF is the factor from step 2).

Factoring By Grouping


Factoring

Example 1:

Step 1: Group

Step 2: Factor out GCF from each group

Step 3: Factor out GCF again


Factoring

Example 2:


Factoring

Try these on your own:


Factoring

Answers:


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