Objective The student will be able to:
16
Objective The student will be able to: factor quadratic trinomials. Trial and Error Method SOL: A.2c Designed by Skip Tyler, Varina High School
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Objective The student will be able to:. factor quadratic trinomials. Trial and Error Method SOL: A.2c. Designed by Skip Tyler, Varina High School. Factoring Chart This chart will help you to determine which method of factoring to use. Type Number of Terms. 1. GCF 2 or more - PowerPoint PPT Presentation
Transcript of Objective The student will be able to:
ObjectiveThe student will be able to:
factor quadratic trinomials.
Trial and Error Method
SOL: A.2cDesigned by Skip Tyler, Varina High School
Factoring ChartThis chart will help you to determine
which method of factoring to use.Type Number of Terms
1. GCF 2 or more
2. Diff. Of Squares 2
3. Trinomials 3
Review: (y + 2)(y + 4) Multiply using FOIL or using the Box Method.Box Method: y + 4
y y2 +4y + 2 +2y +8
Combine like terms.FOIL: y2 + 4y + 2y + 8
y2 + 6y + 8
1) Factor. y2 + 6y + 8Put the first and last terms into the box
as shown.
What are the factors of y2?
y and y
y2
+ 8
1) Factor. y2 + 6y + 8Place the factors outside the box as shown.
y2
+ 8
y
y
What are the factors of + 8?
+1 and +8, -1 and -8
+2 and +4, -2 and -4
The second box works. Write the numbers on the outside of box for your solution.
1) Factor. y2 + 6y + 8Which box has a sum of + 6y?
y2
+ 8
y
y
y2
+ 8
y
y+ 1 + 2
+ 8 + 4
+ y
+ 8y + 4y
+ 2y
1) Factor. y2 + 6y + 8
(y + 2)(y + 4)Here are some hints to help you choose your
factors.
1) When the last term is positive, the factors will have the same sign as the middle term.
2) When the last term is negative, the factors will have different signs.
x2
- 63
2) Factor. x2 - 2x - 63Put the first and last terms into the box
as shown.
What are the factors of x2?
x and x
2) Factor. x2 - 2x - 63 Place the factors outside the box as shown.
x2
- 63
x
x
What are the factors of - 63?
Remember the signs will be different!
2) Factor. x2 - 2x - 63Use trial and error to find the correct
combination!
Do any of these combinations work?
The second one has the wrong sign!
x2
- 63
x
x
+ 21
- 3
+21x
-3x x2
- 63
x
x - 7
+ 9
-7x
+9x
2) Factor. x2 - 2x - 63Change the signs of the factors!
Write your solution.
(x + 7)(x - 9)
x2
- 63
x
x + 7
- 9
+7x
-9x
5x2
+ 14
3) Factor. 5x2 - 17x + 14Put the first and last terms into the box
as shown.
What are the factors of 5x2?
5x and x
3) Factor. 5x2 - 17x + 14
5x2
+ 14
x
5x
What are the factors of + 14?
Since the last term is positive, the signs of the factors are the same! Since the middle term
is negative, the factors must be negative!
3) Factor. 5x2 - 17x + 14 When the coefficient is not 1, you must try
both combinations!
Do any of these combinations work?
The second one! Write your answer.
5x2
+ 14
x
5x
- 7
- 2
- 2x
-35x
5x2
+ 14
x
5x
- 2
- 7
- 7x
-10x
3) Factor. 5x2 - 17x + 14
(5x - 7)(x - 2)
It is not the easiest of things to do, but the more problems you do, the
easier it gets! Trust me!
4) Factor 2x2 + 9x + 10
(x + 2)(2x + 5)
5) Factor. 6y2 - 13y - 5
(2y - 5)(3y + 1)
6) 12x2 + 11x - 5
(4x + 5)(3x - 1)
7) 5x - 6 + x2
x2 + 5x - 6
(x - 1)(x + 6)
