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Factoring Study Guide TEST Friday November 19th
D.O.S. stands for…
Difference of Squares
Example:
Check for D.O.S. Factoring
Does it have 2 terms? Yes/No
Are both numbers perfect squares? Yes/No
Is the sign negative? Yes/No
If you answered yes to all of these, then factor by D.O.S.
x2 – 4
Step 1: Check for D.O.S.
( + )( - )
Step 2: Write your parenthesis, one will be + and one will be -
(x + ) (x - )
Step 3: Break the first term evenly into the parenthesis
(x + 2) (x -2)
Step 4: Break the second term evenly into the parenthesis
1. x2 – 36
(x+6)(x-6)
2. x2 – 121
(x+11)(x-11)
3. 16x2-49
(4x +7)(4x – 7)
4. 4x2 – 1
(2x + 1) (2x – 1)
5. x2 – 9
(x+3) (x-3)
P.S.T. stands for…
Perfect Square Trinomial
Example:
Check for P.S.T. Factoring
Are there three terms? Yes/No
Is the number in front of the first term1? Yes/No
Is the last number a perfect square? Yes/No
If you answered yes to all of these, factor by P.S.T.
x2+4x+4
Step 1: Check for P.S.T.
( + )( + )
Step 2: Write your parenthesis with the correct signs. If the LAST sign is +, both signs will be the same. (This is
determined by the MIDDLE term) If the LAST sign is - the signs will be different.
( x + ) (x + )
Step 3: Break the first term evenly into the parenthesis
( x + 2) (x + 2)
Step 4: Create a T-Chart if needed find the factors of the last number that add up to the middle number.
HINT: If you are factoring a PST both numbers will be the same!
6. x2 +12x +36
(x+6)(x+6)
7. x2 +4x +4
(x+2)(x+2)
8. x2 +10x +25
(x+5)(x+5)
Factoring Trinomials
Check for Trinomial Factoring
Are there 3 terms? Yes/No
Is the number of the 1st term 1? Yes/No
If you answered yes to all of these, use trinomial Factoring.
Examples:
x2 -7 x + 12
(x - _ ) (x - _ )
(x - 3 ) (x - 4)
x2 + x - 12
(x + _ ) (x - _ )
(x + 4 ) (x - 3)
9. x2+ 8x +15
(x+3)(x+5)
10. k2 - 23 k + 42
(k-21)(5-2)
11. a2 +17a + 52
(a+13) (a+4)
12. r2 – 15r – 54
(r-18) (r+3)
13. y2 +20 y + 91
(y+13) (y+7)
Check for Trinomial factoring
If the last number is + you know that both signs will be the same
The sign of the middle terms is what sign you will use.
Create a T-Chart if needed to find the factors of the last number that add up to the middle number.
Check for Trinomial Factoring
If the last number is - you know that both signs will be different.
One sign will be negative, one sign will be positive.
Create a T-Chart if needed find the factors of the last number that add up to the middle number.
Factor By Grouping 1X2 +AB + C
Check for factor by grouping
Are there 4 terms? Yes/No
If you answered yes, factor by grouping.
Example:
2ab + 6ac + 3b + 9c
2ab + 6ac
+ 3b + 9c
GCF: 2a
GCF: 3
2a (b + 3c)
3 (b + 3c)
GCF: ( b + 3c)
(b + 3c) (2a + 3)
14. 2x2 -2x +9x -9
(x-1) (2x+9)
15. 3a2 -5a +3a +5
(3a -5) (a+1)
Step 1: Check for Factor by Grouping
Step 2: If there are 4 terms, separate them into problem into TWO pairs.
Step 3: Factor the GCF from each pairs.
Step 4: Factor out the GCF of both pairs.
Step 5: Next to the GCF write what remains in parenthesis.
Factor By Grouping
AX2 +AB + C
Check to use Factor by grouping
Is the “A” term something other that one? Yes/No
If you answered yes, factor by grouping.
Example:
3x2+8x +5
3x2 +3x +5x + 5
3x2 +3x +5x + 5
GCF: 3x GCF: 5
3x(x+1) 5(x +1)
GCF: (x +1)
(x + 1) (3x + 5)
16. 2x2 + 7x + 3
(x+3) (2x +1)
17. 7x2 +8x + 1
(x+1) (7x +1)
18. 3r2 -2r – 5
(3r -5) (r+1)
19. 5y2 + 4y – 1
(y+1) (5y -1)
20. 3x2 +7x + 2
(x+2) (3x+1)
3• 5 = 15 (a•c)
Find what multiplies together to equal (a•c)
3 + 5 = 8 (b)
Find what adds together to equal (b)
Then replace those numbers for the middle term with an “x” attached
Count the terms, if there are 4 terms separate the problem into TWO pairs.
Factor the GCF from each pairs.
Factor out the GCF of both pairs.
Next to the GCF write what remains in parenthesis.