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Factoring Basics

This document provides a 7-step process for factoring polynomials: 1. Order terms by highest exponent to lowest; 2. Pull out any common factors; 3. Find factors of the first and last terms; 4. See if any factor pairs sum to the middle term; 5. Split the middle term using the factors; 6. Pull common factors from each grouped term; 7. Multiply the factors into binomials.

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61 views9 pages

Factoring Basics

This document provides a 7-step process for factoring polynomials: 1. Order terms by highest exponent to lowest; 2. Pull out any common factors; 3. Find factors of the first and last terms; 4. See if any factor pairs sum to the middle term; 5. Split the middle term using the factors; 6. Pull common factors from each grouped term; 7. Multiply the factors into binomials.

Uploaded by

api-316610413
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PPTX, PDF, TXT or read online on Scribd
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Factoring

The Basics

Step 1
Put the terms in order
Highest order exponent first, followed by
the second highest, etc
Example:
12x + x3 7x2 becomes x3 7x2 + 12x

Step 2
Pull out any shared factors
Example:
x3 7x2 + 12x becomes x (x2 7x + 12)

Step 3
Find the factors of the a value times the c
value
Example:
x (x2 7x + 12)
a = 1 c = 12 a*c = 12

1
2
3

12

12
6
4

1 and 12, 2 and 6, and 3 and 4

Step 4
See if any sets of factors add up to
the b value
Example:
x (x2 7x + 12)
b = -7
1 + 12 = 13; 2 + 6 = 8; 3 + 4 = 7
In this case, because b is negative, both factors
are made negative (-3 + -4 = -7; -3 * -4 = 12)

Step 5
Split the b term and group
Example:

x (x2 7x + 12)
Chosen factors: -3 and -4
x (x2 - 3x + -4x + 12)
x ((x2 - 3x) + (-4x + 12))

Step 6
Pull out common factors from each
group
The remaining terms in each group
should match
Example:
x ((x2 - 3x) + (-4x + 12))
x (x (x 3) + -4 (x 3))

Step 7
Turn the factors into multiplied
binomials
Example:
x (x (x 3) + -4 (x 3))
x (x 4) (x 3)

And now you know how to


factor!
(If a polynomial is not
factorable, use the quadratic
formula)

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