Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
factoring trinomials: ax2 + bx + c pp 138-139, text OBJECTIVE: find the factors of a trinomial of the form ax2 + bx + c factoring trinomials: ax2 + bx + c Review of past lessons factors: numbers or variables that make up a given product GCF: greatest number that could be found in every set of factors of a given group numbers binomial: a polynomial of two terms trinomial: a polynomial of three terms factoring trinomials: ax2 + bx + c Review of past lessons coefficient:the numerical factor next to a variable exponent: the small number on the upper hand of a factor that tells how many times it will used as factor binomial: a polynomial of two terms trinomial: a polynomial of three terms factoring trinomials: ax2 + bx + c Review of past lessons ( x + 4)2 = x2 + 4x + 16 ( b - 3)2 = b2 - 6b + 9 ( y - 5) ( y + 3) = y2 - 2y -15 ( m - 7)( m + 7) = m2 - 49 ( a2+16a+64) = 2 = (a + 8) (a + 8)( a + 8 ) ( 4a2+20a+24) = 4( a2 +5a + 6 ) factoring trinomials: ax2 + bx + c (4a2+20a+24) = 4 ( a2 +5a + 6 ) = 4 (a2 + 5a + 6) = 4 ( a + 3) ( a + 2 ) Example 1. Factor 12y2 – y – 6 12y2 – y – 6 Find the product of the coefficient of the first term (12) and the last term (–6). 12(-6) = -72 Find the factors of -72 that will add up to -1. -72 = -9, 8 -9 + 8 = -1 Use the factors -9 and 8 for the coefficient of the middle term (-1) 12y2 + (– 9 + 8)y – 6 Use the DPMoA 12y2 + (– 9y + 8y) – 6 Remove the parenthesis. 12y2 – 9y + 8y – 6 Group terms that have common monomial factors (12y2 – 9y) + (8y – 6) 3y(4y – 3) Factor each binomial using GCF. + 2 (4y – 3) (4y – 3y) ( 3y + 2) Use the Distributive Property. The factored form of 12y2 – y – 6 Example 2. Factor 3x2 + 4x + 1 3x2 + 4x + 1 3(1) = 3 Find the product of the coefficient of the first term (3) and the last term (1). Find the factors of 3 that will add up to 4. 3 = 3,1 3+1=4 3x2 + (3+ 1)x + 1 3x2 + (3x+ x) + 1 Use the factors 3 and 1 for the coefficient of the middle term (4) Use the DPMoA Remove the parenthesis. 3x2 + 3x + x + 1 (3x2 + 3x) + (x + 1) 3x (x + 1) + (x+1) (x + 1) ( 3x + 1) Group terms that have common monomial factors Factor each binomial using GCF. Use the Distributive Property. The factored form of 3x2 + 4x + 1. Example 3. Factor completely 21y2 – 35y – 56. 21y2 – 35y – 56 7(3y2 – 5y – 8) -24 Factor out the GCF. Factor the new polynomial, if possible. Find the product of 3 and -8. Find the factors of -24 that will add up to -5 which is the middle term. -24 = - 8, 3 Use the -8 + 3 in place of -5 in the middle term. 7[3y2 + (– 8 + 3)y – 8] Remove the parenthesis. 7[3y2 – 8y + 3y – 8] Group terms that have common monomial factors 7[3y2 – 8y + 3y – 8] Group terms that have common monomial factors 7[(3y2 – 8y) + (3y – 8)] Take out the GCF from the first binomial. 7[y(3y – 8) + (3y – 8)] Use the Distributive Property. 7 (3y – 8) ( y + 1) The factored form of 12y2 – y – 6. factoring trinomials: ax2 + bx + c pp 138-139, text Classwork p 163, Practice book homework p 164, Practice book