Factoring Quadratic Equations when a = 1

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Presentation transcript:

Factoring Quadratic Equations when a = 1

FACTORING FACTS This sign comes from multiplying the last terms together when multiplying the polynomials together. If +, then both factors have to be the same. Either + + or - - If -, then signs are different + - This sign also tells us if we are adding or subtracting factors to get the middle term (bx). If +, you are adding. If -, you are subtracting.

# 1 x2 + 7x + 12 Since C is +, both signs have to be the same + & + or - & -. Since b is positive, they are both + Step 1: Fill in x. 12 Step 2: Signs ac + 3 + 4 Step 4: Write the factors b (x+3)(x+4) 7 Step 3: Factors of a•c Since C is +, we are looking for the factors that add to give us 7. 1•12 = 1 • 12 = 2 • 6 = 3 • 4

# 2 12 ac - 2 - 6 b (x-2)(x-6) -8 Factor. x2 - 8x +12 Since C is +, both signs have to be the same + & + or - & -. Since b is negative, they are both - Step 1: Fill in x. 12 Step 2: Signs ac - 2 - 6 Step 4: Write the factors b (x-2)(x-6) -8 Step 3: Factors of a•c Since C is +, we are looking for the factors that add to give us 8. 1•12 = 1 • 12 = 2 • 6 = 3 • 4

# 3 -24 ac - 4 + 6 b (x-4)(x+6) 2 Factor. x2 + 2x - 24 Since C is -, one has to be – and one is +. Step 1: Fill in x. -24 Step 2: Signs ac - 4 + 6 Step 4: Write the factors b (x-4)(x+6) Sign of Larger number 2 Step 3: Factors of a•c 1•24 = 1 • 24 = 2 • 12 = 3 • 8 = 4 • 6 So is it: 4 and -6 or -4 and 6 to give you +2 Since C is -, we are looking for the factors that subtract to give us 2.

# 4 -24 ac - 12 + 2 b (x-12)(x+2) -10 Factor. x2 - 10x - 24 Since C is -, one has to be – and one is +. Step 1: Fill in x. -24 Step 2: Signs ac - 12 + 2 Step 4: Write the factors b (x-12)(x+2) -10 Sign of Larger number Step 3: Factors of a•c 1•24 = 1 • 24 = 2 • 12 = 3 • 8 = 4 • 6 So is it: 2 and -12 or -2 and 12 to give you -10 Since C is -, we are looking for the factors that subtract to give us 10.

Practice Problems (t – 7)(t + 3) (x +8)(x +4) (x-6)(x – 4) Factor each trinomial, if possible. 1) t2 – 4t – 21 2) x2 + 12x + 32 3) x2 –10x + 24 4) x2 + 3x – 18 (t – 7)(t + 3) (x +8)(x +4) (x-6)(x – 4) (x +6)(x – 3)