Warm-Up 2.3 Factor each. 36 – x2 15x4y2 – 20x2y3 + 5x3y4

Lesson 2.3 Algebra 3 Objective: SSBAT factor trinomials. Teacher Algebra 3 Lesson 2.3 Objective: SSBAT factor trinomials. Standards: M11.D.2.2.2

Analyze each. (x + 7)(x + 4) = x2 + 11x + 28 Sum of 7 and 4 Product of 7 and 4 (x + 6)(x – 4) = x2 + 2x – 24 Sum of of 6 and -4 Product of 6 and -4

Recall: Factoring  Rewriting an expression as a Multiplication Problem

Factoring Trinomials of the Form x2 ± bx ± c List the pair of factors for c  If c is positive – the factors will have the same sign  If c is negative – 1 factor will be positive and 1 will be negative 2. Find the pair from above that have a sum of b 3. Write in the form (x ± #)(x ± #) The 2nd number of each will be the factors from step 2

Factored Form: (x + 5)(x + 8) Teacher Examples: Factor each trinomial. 1. x2 + 13x + 40 Factors of +40 The SUM of each 1, 40 2, 20 4, 10 5, 8 41 22 14 13 * You need the pair with a sum of 13, since that is what is in front of the x term. * Therefore use the factors 5 and 8 Factored Form: (x + 5)(x + 8)

(x + 5)(x + 8) = x2 + 8x + 5x + 40 = x2 + 13x + 40 Its Checks. Check  FOIL through and see if you get back to the beginning expression. (x + 5)(x + 8) = x2 + 8x + 5x + 40 = x2 + 13x + 40 Its Checks.

(x – 1)(x – 8) 2. x2 – 9x + 8  Note: the x term is negative: -9x Teacher 2. x2 – 9x + 8  Note: the x term is negative: -9x  Need the negative factors of positive 8 Negative Factors of 8 Sum of each (-9) -1, -8 -2, -4 -9 -6 (x – 1)(x – 8)

Check  FOIL through and see if you get back to Check  FOIL through and see if you get back to the beginning expression. (x – 1)(x – 8) = x2 – 8x – 1x + 8 = x2 – 9x + 8 Checks.

3. y2 – 17y + 42 (y – 3)(y – 14) Negative factors of 42 Teacher 3. y2 – 17y + 42 Negative factors of 42 Sum of each (-17) -1, -42 -2, -21 -3, -14 -6, -7 -43 -23 -17 -13 (y – 3)(y – 14)

Factored Form: (x – 4)(x + 5) Factors of -20 Sum of each (1) 1, -20 -1, 20 2, -10 -2, 10 4, -5 -4, 5 -19 19 -8 8 -1 1 Factored Form: (x – 4)(x + 5)

Factored Form: (x + 2)(x – 7) Factors of -14 Sum of –5 1, -14 -13 -1, 14 13 2, -7 -5 Factored Form: (x + 2)(x – 7)

x2 + 8x + 20 Prime – Cannot Factor

On Your Own. 1. x2 + 14x – 72 2. x2 + 17x + 60

Homework Worksheet 2.3 #1 – 6