5.6 Factoring Trinomials
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Transcript 5.6 Factoring Trinomials
5.6 Factoring Trinomials
ax bx c
2
How to Factor
• 1. Write the trinomial in descending powers of
one variable.
• 2. Factor out any GCF (including (-1) to make
the 1st term positive)
• 3. Test the trinomial for factorability.
2
– Check the value of b 4ac
• If it’s a perfect square, then it’s factorable into 2 different
binomials
• If it’s zero, then it’s factorable and the factors will be the
same
More steps
• 4. When the sign of the 1st term of the trinomial is
positive:
– And the sign of the 3rd term is positive, the signs in each
parentheses will be the same
x 6x 5 x 5 x 1
2
– And the sign of the 3rd term is negative, the signs in each
parentheses will be different
x 6x 7 x 7 x 1
2
More steps continued
• 5. Try different combos until you find the one
that works.
– If the leading coefficient is 1
• Pick the factorization where the sum of the factors of c is
equal to the coefficient of the middle term (b)
– If the leading coefficient is not 1
• Can use trial and error
• Can use the key method
Step 5 Cont’d (Key Method)
• i. Find product of ac (this is the key #)
• ii. Find 2 factors of the key # whose sum is b
• iii. Use the factors of the key # as coefficient of 2
2
terms to be placed between ax and c
• iv. Factor using grouping
Example of key method
15a 17 a 4
2
i. ac 15 4 60
ii. factors of 60 that add up to 17
20 and 3
iii. 15a 3a 20a 4
2
iv. 3a 5a 1 4 5a 1
5a 1 3a 4
• 6. Check by multiplying out.
Another example – key method
6 x 17 x 12
2
i. ac 6 12 72
ii. factors of 72 that add up to 17 (b term)
9 and 8
iii. 6 x 9 x 8x 12
2
iv. 3x 2x 3 4 2x 3
2x 33x 4
Using Substitution to Factor
x y
Let
2
7 x y 12
x y z
z 7 z 12
2
z 3 z 4
Resubtitute:
x y 3 x y 4
Using Grouping to Factor Trinomials
10 x 13x 3
2
10 x 15x 2 x 3
2
10 x
2
15 x 2 x 3
5x 2x 3 2x 3
2x 35x 1