Factoring Trinomials 3Trinomial – 3 terms. second termthird termWhen factoring a trinomial, we need to look at the second term and the third term to help find the factors. The factors of a trinomial will be two binomials.The factors of a trinomial will be two binomials.

Chart to Help with Signs Sum (2 nd Term) Product (3 rd Term) INTEGERS NegativeNegative Bigger #(-) Smaller # (+) NegativePositive Both Negative numbers PositiveNegative Bigger # (+) Smaller # (-) PositivePositive Both Numbers Positive

Let’s take a Look x 2 + 7x + 6 What two numbers add up to +7 Same two numbers that multiply to give you +6 Therefore: x 2 + 7x + 6 = (x + 1)(x + 6)

Let’s take a Look a 2 – 8a + 12

Let’s take a Look m 2 – 5m - 14

Let’s take a Look Simplify, then Factor: -5r -3r r 2 – 3 – 3r -3r 2 + 4r 2 – 5r – 3r + 15 – 3 r 2 – 8r + 12 What two numbers add up to - 8 Same two numbers that multiply to give you + 12 Therefore: r 2 – 8r + 12 = (r -2)(r - 6) Factors:Sum: 1 x x x 6 -2 x -6 3 x x = (-12) = = (-6) = (4) = (+4) = + 7

Let’s take a Look Factor Completely: 7q 2 – 14q -21 7(q 2 – 2q – 3) What two numbers add up to - 2 Same two numbers that multiply to give you - 3 Therefore: 7(q 2 – 2q – 3) = 7(q + 1)(q - 3) Factors:Sum: 1 x 3 -1 x = (-3) = (-3) = (3) = 2 Because the first term is not a one, consider factoring out the GCF

Let’s take a Look Factor Completely: 3x x (x 2 + 7x + 19) What two numbers add up to 7 Same two numbers that multiply to give you 19 Therefore: 3(x 2 + 7x + 19) = 3(x 2 + 7x + 19) Because 19 is a prime and 1 and 19 can not give a sum of 7, we can not factor any further.

y 2 + 6y + 9 a 2 – 5a + 4 m 2 – m - 12 FACTOR COMPLETELY

SIMPLIFY, FACTOR COMPLETELY -5x + 5x x 2 – 3 – 3x 6y 2 – 12y - 18

Class work Worksheet 3-10bWorksheet 3-10b