Factor Trinomials 8-4 page 107, example 1 2x 2 – 15x+ 18 When the last term is positive, what are the signs? Both positive? Both negative? Mixed? (+)(+)

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Presentation transcript:

Factor Trinomials 8-4 page 107, example 1 2x 2 – 15x+ 18 When the last term is positive, what are the signs? Both positive? Both negative? Mixed? (+)(+) (-)(-) (+)(-)

Factor Trinomials 8-4 page 107, example 1 2x 2 – 15x+ 18 The last term is positive, so the signs are the same. The middle term is negative so: Both signs are negative. (-)(-)

Factor Trinomials 8-4 page 107, example 1 2x 2 – 15x+ 18 Both signs are same, negative. (-)(-) But the first term has a coefficient of 2. Multiply 2 times 18.

Factor Trinomials 8-4 page 107, example 1 2x 2 – 15x+ 18 Both signs are negative. 2 times 18 is 36 What multiplies to 36 and adds to 15?

Factor Trinomials 8-4 page 107, example 1 2x 2 – 15x+ 18 What multiplies to 36 and adds to 15? 36x1 check x2 check x3 check found it! Use -12 and -3 because both signs are negative

Factor Trinomials 8-4 page 107, example 1 2x 2 – 15x+ 18 What multiplies to 36 and adds to 15? 12x3= =15 (x-12)(x-3) Both signs negative Use the 2 from the first term as a denominator.

Factor Trinomials 8-4 page 107, example 1 2x 2 – 15x+ 18 (x-12)(x-3) 2 2 Reduce if possible. (x-6)(x-3) 2 Does not reduce so: (x-6)(2x-3)

Factor Trinomials 8-4 page 107 #1 2x 2 – 3x – 2; 2x2 = 4; Mult to 4; sub to 3 (x-4)(x+1) Mixed signs 2 2 Reduce if possible. (x-2)(x+1) 2 Does not reduce so: (x-2)(2x+1)

Factor Trinomials 8-4 page 107 #7 2a 2 + 5a + 3; 2x3 = 6; Mult to 6; adds to 5 (x+3)(x+2) Same signs 2 2 Reduce if possible. (x+3)(x+1) 2 Does not reduce so: (2x+3)(x+1)

Factor Trinomials 8-4 page 107 #10 8x 2 – 4x – 24; Factor out 4 4(2x 2 – x – 6); 2times6=12; Multiplies to 12; subtracts to – 1. 2(x+3)(x- 4) Mixed signs 2 2 Reduce if possible. 2(x+3)(x-1) 2 Does not reduce so: (2x+3)(x-1)

Factor Trinomials 8-4 page 107 #13 3y 2 – 6y – 24; Factor out 3 3(y 2 – 2y – 8); Multiplies to 8; subtracts to – 2. 3(y+2)(y-4)=0 mixed signs

Factor Trinomials 8-4 page 108 #1 8x 2 + 2x – 3; Check for GCF: none 8 times 3 = 24; Mult to 24; subtracts to 2. 24x1;12x2; 8x3; 6x4; use 6 and 4. (x+6)(x - 4) becomes(x+3)(x – 1) Move denominator to front (4x+3)(2x - 1)

Factor Trinomials 8-4 page 108 #1 (4x+3)(2x - 1) = 0 Solve: 4x+3= 0 2x - 1= 0 x = -3 x = 1 4 2