Transcript Step one

Warm up
• Factor the Greatest common factor out of
the following polynomials
• 4x2 + 8x + 16
• 6x2 + 12x
2x2 + 3x
Greatest common Factor
• Coefficients – numbers before the variables
– Look at coefficients and consider largest
number that can divide into all of them
• Variables – letters that represent more than
one possible value
– Look for smallest exponent that all terms have
in common
Factor by taking the GCF
• 4x2 + 20x – 16
3x3 + 2x2 + 7x
• 3x2 + 6x
7x2 + 35x – 14
Factoring Trinomials
Step one – write factors of last term
Step two – find the factors that add to get you middle number
Step three – write factors you found as binomials
2
X
+ 8x + 12
Factoring Trinomials
Step one – write factors of last term
Step two – find the factors that add to get you middle number
Step three – write factors you found as binomials
2
X
+ 8x + 15
Factoring Trinomials
Step one – write factors of last term
Step two – find the factors that add to get you middle number
Step three – write factors you found as binomials
2
X
- 4x + 3
Factoring Trinomials
Step one – write factors of last term
Step two – find the factors that add to get you middle number
Step three – write factors you found as binomials
2
X
- 5x + 6
Factoring Trinomials
Step one – write factors of last term
Step two – find the factors that add to get you middle number
Step three – write factors you found as binomials
2
X
+ 2x - 8
Factoring Trinomials
Step one – write factors of last term
Step two – find the factors that add to get you middle number
Step three – write factors you found as binomials
2
X
- x - 12
Factor These Trinomials!
Factor each trinomial, if possible. The first four do NOT have
leading coefficients, the last two DO have leading coefficients.
Watch out for signs!!
1)
2
t
– 4t – 21
2) x2 + 12x + 32
3) x2 –10x + 24
4) x2 + 3x – 18
Factoring Trinomials
Returning to the FOIL method,
F
O
(3x + 2)(x + 4) =
I
L
Factoring Polynomials where the
lead coefficient isn’t one
• Example
• 6x2 + 5x – 4
Factoring polynomials where the
lead coefficient isn’t one
• 1) multiply first coefficient with the last
coefficient
• 2) list the factors of that multiplication
• 3) Find the factors that add to the middle term
• 4) List out 4 terms
• 5) factor by grouping
•
•
•
•
•
1) multiply first coefficient with the last coefficient
2) list the factors of that multiplication
3) Find the factors that add to the middle term
4) List out 4 terms
5) factor by grouping
2x2 + 7x + 3
•
•
•
•
•
1) multiply first coefficient with the last coefficient
2) list the factors of that multiplication
3) Find the factors that add to the middle term
4) List out 4 terms
5) factor by grouping
3x2 - 8x + 4
Factoring Polynomials where the
lead coefficient isn’t one
• Example
• 2x2 - 11x + 15
Factoring Polynomials where the
lead coefficient isn’t one
• Example
• 3x2 + 7x - 20
Types of factoring
• Greatest common factor
• Factoring a trinomial a = 1
• Factoring a trinomial a ≠ 1
Factor the following polynomials
*** Always look for a GCF
(greatest common factor) first
4x2 + 16x + 12
Factor the following polynomials
*** Always look for a GCF
(greatest common factor) first
2x2 + 6x + 8
Factor the following polynomials
*** Always look for a GCF
(greatest common factor) first
4x2 - 20x + 24