Factoring Polynomials

Factoring Polynomials

You know how to DISTRIBUTE…

4(x + 3) 4x + 12

Factoring Polynomials is like doing “Reverse Distribution”.

4 + 20 12x (3x 5) 4

You try it. Separate out the factors. What is the LARGEST number can divide out of 45 & 18 ?

(45x + 18)

“9” and “(5x + 2)” are FACTORS of “(45x + 18)”

9 (5x + 2)

Trog thought “Factors” are just numbers!!

“Factors” can be numbers… 45: 9 • 5

9 & 5 are FACTORS of 45

“Factors” can be variables (letters)… x 2y 4z 3: x • x • y • y • y • y • z • z • z

These are all FACTORS

Factors can also be a mix of variables and numbers… 12x3y2: 2 • 2 • 3 • x • x • x • y • y

FACTORS: all the numbers and variables that multiply up to make the larger term

Here is the part that confuses many people, because nobody tells them…

Factors can also be whole GROUPS! What number can be divided out?

(12x + 18)

FACTORS !

(6) (2x + 3)

Factor these!

(10x – 25) : ( 5 )( 2x - 5 ) (50y + 75) : (25)( 2y + 3 )

You can even take out a common variable…watch:

x + x) x = ( (x 2

UN-Distribute !

) (x + 1)

How to Un-Distribute (factor): STEPS

MATH

(16x + 4) 4

4

(4) (4x + 1)

1. Figure out the GCF of both numbers & write it. 2. Divide out the GCF from each of the terms, and write the new group. 3. Check to see if you are done.

MATH

(3x2 + 9x) 3x

3x

(3x)(x + 3)

STEPS

1. Find the GCF and write it 2. Divide out the GCF from each term, and write the new group. 3. Are you done?

FACTOR BY GROUPING

Sometimes all the numbers don’t have a GCF to use. Just group up ( x2 + 2x)+(3x + 6 ) the terms and undistribute from each group!

x(x + 2) + 3(x + 2)

Now, group x(x + 2) + 3(x + 2) the WHOLE THING !!

(

)

Do you see something we can UNDISTRIBUTE again?

( x(x + 2) + 3(x + 2) ) (x + 2) (x + 3)

UNDISTRIBUTE the matching group.

Write what’s left!

A C T O R E D !!

6a – 15a – 8a + 20 2

(6a2 – 15a )+(-8a + 20) (6a2 – 15a) + (-8a + 20)

To make things easier, make the minus in the middle an addition. Now you can group them Next factor each group & finish up…