1. Section 1.6 Factoring Trinomials
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2. What are trinomials? A trinomial will have 3 terms
There are four steps used to factor each of them
Check for a common monomial factor
Look for special cases
Factor by trial and error
Continue factoring as long as possible

3. Check for a common factor
For each trinomial, it simplifies the factoring process if you look for a common factor
What is the common factor in this expression?
x2 – x +
Since each term is divisible by 2, the 2 is common
Each term also contains a y, so the common monomial is 2y
When factored: 2y ( x2 – 4x + 4 ) 2 y 8 y 8 y

4. What is the common factor?
find the common factor, then check your answer
3x2y3 – 6x5y + 12x3z
3x2
14a2b2c2 + 7a3b3c3d + 21ab2c
7ab2c
answer:
answer:

5. Check for special cases
Once all of the common factors have been removed, look for special cases
The only special case we’ll look at here is the perfect square trinomial
a2 + 2ab + b2

6. 2. Check for special cases
If there is a perfect square, the first and last terms must be perfect squares
x2 + 4x + 4
The first term ( x2 ) and last term ( 4 ) are both perfect squares

7. 2. Check for special cases
a perfect square will also need to have a specific middle term
take the square root of the first term, multiply it by the square root of the last term, then multiply that by 2

8. 2. Check for special cases
x2 + 4x + 4
in this equation, the square root of the first term is x
the square root of the last term is 2
when multiplied, x ( 2 ) ( 2 ) = 4x
since this matches the middle term in the original expression, this is a perfect square

9. 2. Check for special cases
x2 + 4x + 4
the factors for this will follow the pattern:
( x + 2 ) 2
the first number inside of the brackets is the square root of the first term, the second number is the square root of the last term
the sign inside of the brackets will match the sign of the second term

10. Which of these are perfect squares?
4x2 + 16x + 25
8x2 + 16x + 9
x2 - 12x + 36
81x2 + 38x + 100
9x2 + 25x + 4
16x2 + 32x + 3
2x2 + 10x + 25
4x2 + 12x - 9

11. 3. factor by trial and error
if the expression is still not factored completely, you must factor by trial and error

12. 3. factor by trial and error
3x x + 8
to factor, you need all of the factors of the first and last terms
first term: 1 x 3
last 1 x 8 , 2 x 4
these need to be combined until the correct set of factors is obtained

13. 3. factor by trial and error
3x x + 8
remember, if the last term is positive, both of the factors have the same sign
if the second term is negative, then both are negative
if it is positive, then both are positive
if it is negative, then they have opposite signs

14. 3. factor by trial and error
3x x + 8
since there are only 2 factors for the first term, we can easily guess the first part of the 2 factors
( 3x ) ( x )
we also know that the signs inside of the brackets are negative, since the sign of the second term was negative, but the third term was positive - -

15. 3. factor by trial and error
3x x + 8
( 3x ) ( x )
Now we must choose two factors of 8 and see if we obtain the correct answer
This might take a few attempts.

16. 3. factor by trial and error
3x x + 8
( 3x ) ( x )
When multiplied, we get:
3x2 - 24x - x + 8
This is not the correct answer.

17. 3. factor by trial and error
3x x + 8
( 3x ) ( x )
We don’t need to do all of the steps of FOIL, we only need the middle term, so we only multiply the outside and inside terms

18. 3. factor by trial and error
3x x + 8
( 3x ) ( x )
Lets try two different factors.
When multiplied, we get:
-6x - 4x
Combined together, we have -10x
These are now the correct factors 4 2

19. 4. Continue factoring until reach factor is prime
Remember to apply as many steps as needed until the trinomial is factored as much as possible