Factoring Trinomials When a 1.

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Presentation transcript:

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. 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 + 8 Create 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) Factor. 3y2 + 14y + 8 ( x + 12) (x + 2) now divide or reduce 12 and 2 by your a (a= 3) ___ ___ 3 3 ( x + 12) (x + 2) *After you reduce, if there is a number left in the denominator, you take it to the front of the factor.

___ ___ ( x + 12) (x + 2) 3 3 = ( x + 4) (3x + 2) y

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)

___ ___ 5 5 ( x - 10) (x – 7) *After you reduce, if there is a number left in the denominator, you take it to the front of the factor. =( x - 2) (5x – 7)

FACTORING 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)

1st Step: Check to Factor GCF 12y2 - 26y – 10 ****Do not forget** 1st Step: Check to Factor GCF GCF: 2 2( 6y2 - 13y – 5)

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

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) ___ ___ 6 6 2 ( y + 1)( y – 5) ___ ___ 3 2 2(2y-5)(3y+1)

5) -12x2 - 11x + 5 -(3x-1)(4x+5) 6) 5x - 6 + x2 1st reorder: x2 + 5x - 6 (x-1)(x+6)