Factoring Trinomials
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Factoring Trinomials When a 1. Factoring Chart This 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 Trinomials 3 Grouping 4. Review: (3y + 2)(y + 4) Multiply using FOIL. FOIL:

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Factoring Trinomials When a 1

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Factoring trinomials when a 1

Factoring Trinomials

When a 1


Factoring trinomials 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

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.


Factoring trinomials when a 1

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 3 y 2 14y 8 create a table as shown below

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


Factor 3 y 2 14y 8

( x + 12) (x + 2)

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

Factor. 3y2 + 14y + 8

___

___

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.


Factoring trinomials when a 1

___

___

( x + 12) (x + 2)

3

3

= ( x + 4) (3x + 2)

y


Factoring trinomials when a 1

  • 2) Factor. 5x2 - 17x + 14

  • Factors of: Multiply the 1st and

  • last coefficients.

  • Sum of: Middle Term

  • Factors of +70 Sum of -17


Factoring trinomials when a 1

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)


Factoring trinomials when a 1

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

___

___

5

5

=( x - 2) (5x – 7)


Factoring trinomials when a 1

FACTORING

QUIZ


Factoring trinomials when a 1

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)


Factoring trinomials when a 1

  • 12y2 - 26y – 10

  • ****Do not forget**

  • 1st Step: Check to Factor GCF

  • GCF: 2

  • 2( 6y2 - 13y – 5)


Factoring trinomials when a 1

2( 6y2 - 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


Factoring trinomials when a 1

2( 6y2 - 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 2 y 2 y 15

Now reduce by the a term (a = 6)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)


Factoring trinomials when a 1

5) -12x2 - 11x + 5

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

6) 5x - 6 + x2

1st reorder: x2 + 5x - 6

(x-1)(x+6)


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