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Title: Factoring
Description: Perhaps one of the most important skills to master in all of higher level math. This is the best set of notes i have seen and it explains it perfectly.
Description: Perhaps one of the most important skills to master in all of higher level math. This is the best set of notes i have seen and it explains it perfectly.
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Factoring Notes
To factor a number is to express the number as a PRODUCT of numbers
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If you are asked to factor, the answer must be a PRODUCT and the answer must be ONE
TERM
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STEPS FOR FACTORING:
STEP 0: ORDER!
• "Check the flow!"
• The terms must be in order of decreasing degree of the variable that comes first in the
alphabet
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• The lead term of the polynomial must be POSITIVE
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STEP 1: FACTOR OUT THE GREATEST COMMON FACTOR!
• The GCF must be in EVERY term
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Look for:
□ The numerical GCF
□ The variable GCF
□ The polynomial GCF
○ On the next line, write down the GCF and immediately after the GCF place
grouping symbols
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THE NUMBER OF TERMS IN THE GROUPING SYMBOLS MUST
MATCH THE NUMBER OF TERMS IN THE POLYNOMIAL
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Chapter 4 Page 1
When finished with STEPS 0 and 1, think about the number of terms you have left in the
polynomial factors
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If it is a TRINOMIAL (3 terms), then refer to STEP 3
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STEP 2: FACTORING BINOMIALS!
• There are only three ways to factor binomials
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• Follow the order of the special patterns:
○ (A) First check for DIFFERENCE OF TWO SQUARES
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○ (C) Third check for SUM OF TWO CUBES
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STEP 2A - Difference of 2 Squares
The difference of two squares factors into the product of conjugates!
STEP 2B: DIFFERENCE OF TWO CUBES
STEP 3 - Factoring TRINOMIALS
STEP 3A - PERFECT SQUARE TRINOMIAL FACTORS INTO THE SQUARE OF
BINOMIAL
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• The middle term must be the PRODUCT of:
○ 2 TIMES the square root of the first term TIMES the square root of the last term
STEP 3B: Factor using FOIL in reverse
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Two methods:
• Both involve grouping the terms of the polynomials
• Remember you can reorder the terms - commutative property
• Remember you can introduce parentheticals to group the terms - associative property
(A) Group as a perfect square trinomial MINUS a perfect square monomial
(B) Group as two pairs of binomials separated by an addition symbol
Examples of Method (A)
Chapter 4 Page 3
Examples of Method (B)
Chapter 4 Page 4
Title: Factoring
Description: Perhaps one of the most important skills to master in all of higher level math. This is the best set of notes i have seen and it explains it perfectly.
Description: Perhaps one of the most important skills to master in all of higher level math. This is the best set of notes i have seen and it explains it perfectly.