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Factoring Trinomials When a 1PowerPoint Presentation

Factoring Trinomials When a 1

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### Factor. 3y2 + 14y + 8

When a 1

Factoring ChartThis chart will help you to determine which method of factoring to use.TypeNumber of Terms

1. GCF 2 or more

2. Diff. Of Squares 2

- Trinomials 3
- Grouping 4

Review: (3y + 2)(y + 4)Multiply using FOIL.

FOIL:

Combine like terms.

3y² + 12y + 2y + 8 =

3y² + 14y + 8

y² + (12 + 2)y + (2)(12)

How would you get 24 from the 2nd step?

*You need the factors of ac that add to = b.

ax2 + bx + c * If p and q are factors of ac that add to = b and p > q. ax2 + bx + c ax2 - bx + c (x+p)(x+q) (x-p)(x-q) ax2 + bx – c ax2 – bx - c (x+p)(x-q) (x-p)(x+q)

1) Factor. 3y2 + 14y + 8Create a table as shown below.

Factors of ac: Multiply the 1st and last coefficients: 3(8) = 24

Sum of b: Middle coefficient: 14

Factors of +24 Sum of +14

1, 24

2, 12 2 + 12 = 14*

3, 8

4, 6

now divide or reduce 12 and 2 by your a (a= 3)

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3

3

( x + 12) (x + 2)*After you reduce, if there is a numberleft in the denominator,you take it to the front of the factor.

- 2) Factor. 5x2 - 17x + 14
- Factors of: Multiply the 1st and
- last coefficients.
- Sum of: Middle Term
- Factors of +70 Sum of -17

Factor. 5x2 - 17x + 14

Factors of +70 Sum of -17

-10, -7 -10 + -7 + -17

( x - 10) (x – 7)

now reduce 10 and 7 by your a (a= 5)

( x - 10) (x – 7)*After you reduce, if there is a numberleft in the denominator,you take it to the front of the factor.

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5

5

=( x - 2) (5x – 7)

QUIZ

It is not the easiest of things to do, but the more problems you do, the easier it gets! Trust me!

3) Factor. 2x2 + 9x + 10

(2x + 5)(x + 2)

- 12y you do, the easier it gets! Trust me!2 - 26y – 10
- ****Do not forget**
- 1st Step: Check to Factor GCF
- GCF: 2
- 2( 6y2 - 13y – 5)

2( 6y you do, the easier it gets! Trust me!2 - 13y – 5)

Now we need to find the factors of ac that + to = b

Factors of ac: a=6 and c = -5

so ac = -30.

Sum of b: -13

2( 6y you do, the easier it gets! Trust me!2 - 13y – 5)

Factors of -30 Sum of -13

1, -30

2, -15 2 + -15 = -13

3, -10

5, -6

Now reduce by the a term (a = 6) you do, the easier it gets! Trust me!2(y + 2)(y – 15)

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6

6

2 ( y + 1)( y – 5)

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3

2

2(2y-5)(3y+1)

5) -12x you do, the easier it gets! Trust me!2 - 11x + 5

-(3x-1)(4x+5)

6) 5x - 6 + x2

1st reorder: x2 + 5x - 6

(x-1)(x+6)

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