factoring trinomials: a x 2 + bx + c OBJECTIVE:  f ind the factors of a trinomial of the form ax 2 + bx + c pp , text

factoring trinomials: ax 2 + bx + c  f actors: Review of past lessons numbers or variables that make up a given product greatest number that could be found in every set of factors of a given group numbers  G CF:  b inomial:a polynomial of two terms  t rinomial:a polynomial of three terms

factoring trinomials: ax 2 + bx + c  c oefficient: Review of past lessons the numerical factor next to a variable the small number on the upper hand of a factor that tells how many times it will used as factor  e xponent:  b inomial:a polynomial of two terms  t rinomial:a polynomial of three terms

factoring trinomials: ax 2 + bx + c ( x + 4) 2 Review of past lessons = x 2 + 4x+ 16 ( b - 3) 2 = b 2 - 6b+ 9 ( y - 5) ( y + 3) = y 2 - 2y-15 ( m - 7) ( m + 7)= m ( a 2 +16a+64) = ( )( ) aa = (a + 8) 2 ( 4a 2 +20a+24)= 4 ( ) a 2 +5a+ 6

factoring trinomials: ax 2 + bx + c (4a 2 +20a+24) = 4 ( ) a 2 +5a + 6 (a 2 + 5a + 6)= 4 = 4 ( ) ( ) a a

Example 1. Factor12y 2 – y – 6 Find the product of the coefficient of the first term (12) and the last term (–6). 12y 2 – y – 6 Find the factors of -72 that will add up to (-6) = = -9, = -1 Use the factors -9 and 8 for the coefficient of the middle term (-1) 12y 2 + (– 9 + 8)y – 6 Use the DPMoA 12y 2 + (– 9y + 8y) – 6 Remove the parenthesis.

(4y – 3)Use the Distributive Property. 3y The factored form of 12y 2 – y – 6 12y 2 – 9y + 8y – 6 Group terms that have common monomial factors (12y 2 – 9y) + (8y – 6) Factor each binomial using GCF. 3y(4y – 3)+ 2 (4y – 3y) ( ) + 2

Example 2. Factor 3x 2 + 4x + 1 Find the product of the coefficient of the first term (3) and the last term (1). 3x 2 + 4x + 1 Find the factors of 3 that will add up to 4.3(1) = 3 3 = 3, = 4 Use the factors 3 and 1 for the coefficient of the middle term (4) 3x 2 + (3+ 1)x + 1 Use the DPMoA 3x 2 + (3x+ x) + 1 Remove the parenthesis.

+ (x+1)Use the Distributive Property. (x + 1) The factored form of 3x 2 + 4x x 2 + 3x + x + 1 Group terms that have common monomial factors (3x 2 + 3x) Factor each binomial using GCF. (x + 1)+ (x + 1)3x 3x( ) + 1

Example 3. Factor completely 21y 2 – 35y – 56. Factor out the GCF. Factor the new polynomial, if possible. Find the product of 3 and [3y 2 + (– 8 + 3)y – 8] Remove the parenthesis. 21y 2 – 35y – 56 7(3y 2 – 5y – 8) Find the factors of -24 that will add up to -5 which is the middle term. -24 = - 8, 3 Use the in place of -5 in the middle term. 7[3y 2 – 8y + 3y – 8] Group terms that have common monomial factors

Use the Distributive Property. 7The factored form of 12y 2 – y – 6. Group terms that have common monomial factors 7[(3y 2 – 8y) + (3y – 8)]Take out the GCF from the first binomial. 7[3y 2 – 8y + 3y – 8] 7[y(3y – 8) + (3y – 8)] ( ) y (3y – 8) + 1

factoring trinomials: ax 2 + bx + c Classwork p 163, Practice book pp , text homework p 164, Practice book