Transcript FACTORING REVIEW

FACTORING REVIEW
Math 0099
Chapter 6
Created and Presented by
Laura Ralston
STEP 1
Always check to see if you have
a Greatest Common Factor
(GCF). If so, remove it from the
problem first.
 The GCF is a number, letter, or combination
thereof in each term of the problem.
 If the leading coefficient is negative, factor
out a -1
STEP 2
Depends on the number of terms
the polynomial contains
A) If the polynomial has 2 terms, check
to see if it is a difference of two
squares by asking yourself three
questions.
THE QUESTIONS
 Is the first term squared?
 Is the second term squared?
 Is there a minus sign between terms?
 You must answer YES to all three to
proceed.
Difference of Two Squares
2
2
a - b = (a + b) (a - b)
STEP 2 , Part B)
 If you have 4 terms, you will use grouping
technique.
 Break the problem into 2 smaller problems
by considering the first two terms as one
and the second two terms as another.
 Look for GCF in each pair. Once you have
removed the GCF from each pair, the
expression in the parentheses should be
the same. It is now the GCF.
STEP 2, Part C)
 If you have 3 terms, rewrite the polynomial
with 4 terms and use the grouping
technique (ac method) or trial and error
technique
 For ac method:
• Multiply the coefficient on the squared term
and the constant.
• List the pairs of numbers that will give you that
product
Continued…..
• Using the sign in front of the constant, decide
which pair will give you the coefficient on the
middle term.
• Rewrite and use grouping technique by
replacing the middle term with the pair you
selected.
STEP 3
 As a final check, see if any of the factors
you have written can be factored further. If
you have overlooked a common factor, you
can catch it here.
 Rule of thumb:
exponents on variable will
most often be 1.
STEP 4
If nothing will factor, the
polynomial is PRIME.
Move on to the next problem
Examples

1) a2 – 4a + 3

2) y2 + 8y + 15
Examples

3) x2 + 3x - 10

4) m2 – m - 6
Examples

5) y2 - 49

6) 49x2 + 4
Examples

7) -2y2 + 24y - 70

8) 3n3 + 15n2 + 18n
Examples

9) 14 + 11x – 15x2

10) 252x – 175x3
Examples

11) 2xz + 10x + z + 5

12) 2x3 – 14x2 – 3x + 21
Assignment
Page 479 #1-65 odd