Transcript Factoring Review - Central High School

Factoring Review
Binomials
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Look for the Greatest Common Factor
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18x + 27
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GCF = 9
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9(2x + 3)
Binomials
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No GCF look for the difference of squares
x 9
2
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This means that the two terms of the binomial
are perfect squares and there is a minus sign
between them.
Binomials
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You are done factoring a binomial:
• When you have the sum of squares
• When there are no more perfect squares
• When there is no longer a squared term
Trinomials
• Look for the GCF
• Determine what the signs are
– If the last term is positive the signs are both
the same as the middle term
– If the last term is negative the signs are
opposite (one is positive and one is negative)
Trinomials
• Look at the first term. If there is not a
number in front of the squared term then
you only need to look at factors of the last
term that will add or subtract to get the
middle term.
Trinomials
x  10x  16
2
• (x + 8)(x + 2)
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List Factors of 16
16,1
4,4
8,2
Which ones add together
to give you 10?
Trinomials
x  5 x  36
2
• (x – 9)(x + 4)
• List Factors of – 36
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-1,36
-36,1
-12,3
-3,12
-18,2
-2,18
-4,9
-9,4
-6,6
Which pair add up to – 5?
Trinomials
• Look at the first term. If there is a
number in front of the squared term, you
must look at factors of the first term and
the last term. If there is a small amount
of factors you can easily guess and check.
Trinomials
• This is the long way, but
this always works!
6 x  17x  12
2
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First multiply 6 by 12
Find factors of 72
36,2
24,3
4,18
6,12
8,9
Which pair add to get 17?
Trinomials
• Break the 17x into the
two numbers
6 x  8 x  9 x  12
2
• Then Group the 1st
two terms and the
last two terms.
(6 x  8x)  (9 x  12)
2
Trinomials
• Factor out the GCF in each set of
parenthesis.
• 2x(3x + 4) + 3(3x + 4)
• Both sets of numbers in the parenthesis
have to be exactly the same to continue.
Trinomials
• The numbers in front of the parenthesis
make up one factor and the parenthesis
make up the other factor.
• (2x + 3)(3X + 4)
Trinomials
• Always factor completely!
– You may have binomials that can be factored
further.