Factoring Quadratic Equations

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Presentation transcript:

Factoring Quadratic Equations

Find the factors of c that add to b Factoring Quadratic Equations Remember: Quadratic Equations have a degree of 2 Quadratics ax2 + bx + c Find the factors of c that add to b “Factors” are the numbers you multiply to get another number 1 x 6 and 2 x 3 The (+) factors of 6 are: The (-) factors of 6 are: -1 x -6 and -2 x -3

How to Factor Quadratic Equations Example 1 x2 + x + 7 7 12 12 1 x 12 =12 -1 x -12 = 12 2 x 6 = 12 -2 x -6 = 12 3 x 4 = 12 -3 x -4 = 12 Write down all the factor pairs of ___. 1 Positive Negative From this list, choose the pair that adds up to ___ 2 3 + 4 = 7 (x + 3)(x + 4) (x + )(x + ) 3 Put these numbers into brackets

How to Factor Quadratic Equations Example 2 x2 + x + 6 6 8 8 1 x 8 =8 -1 x -8 = 8 2 x 4 = 8 -2 x -4 = 8 Write down all the factor pairs of ___. 1 Positive Negative From this list, choose the pair that adds up to ___ 2 2 + 4 = 6 3 Put these numbers into brackets (x + 2)(x + 4)

How to Factor Quadratic Equations Example 2 x2 x -3 -3 -4 -4 -1 x 4 = -4 -2 x 2 = -4 1 x -4 = -4 2 x -2 = -4 Write down all the factor pairs of ___. 1 From this list, choose the pair that adds up to ___ 2 1 + -4 = -3 3 Put these numbers into brackets (x - 4)(x + 1)

1 x2 + 5x + 6 2 x2 - x – 6 3 x2 + 8x + 12 4 x2 + x – 12 5 x2 - 8x + 15 7 x2 - 3x – 18 8 x2 - 10x – 24 9 x2 + 8x + 16 10 x2 - 4x – 60

1 x2 + 5x + 6 (x + 3)(x + 2) 2 x2 - x – 6 (x – 3)(x + 2) 3 4 x2 + x – 12 (x – 3)(x + 4) 5 x2 - 8x + 15 (x – 3)(x – 5) 6 x2 + 3x – 21 Does Not Factor 7 x2 - 3x – 18 (x – 6)(x + 3) 8 x2 - 10x – 24 (x - 12)(x + 2) 9 x2 + 8x + 16 (x + 4)(x + 4) 10 x2 - 4x – 60 (x - 10)(x + 6)

(x - 3) (x - 2) x(x - 2) -3(x - 2) x(x) + x(-2) - 3(x) - 3(-2) Factor the following: x2 - 5x + 6 = Solution: x2 - 5x + 6 = (x - 3) (x - 2) (x - 3) (x - 2) x(x - 2) -3(x - 2) x(x) + x(-2) - 3(x) - 3(-2) x2 - 2x - 3x + 6 x2 - 5x + 6 Factor: Factor: Combine like terms: