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5.3 – Solving Quadratic Equations by Factoring

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Ex. 1 Solve y = x 2 + 5x + 6 by factoring.

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x 2 + 5x + 6 = y

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Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0

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Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0

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Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0

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Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0

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Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0 x + 2 = 0

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Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0 x + 2 = 0

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Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0 x + 2 = 0ORx + 3 = 0

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Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0 x + 2 = 0ORx + 3 = 0 -2 -2

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Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0 x + 2 = 0ORx + 3 = 0 -2 -2 x = -2

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Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0 x + 2 = 0ORx + 3 = 0 -2 -2 -3 -3 x = -2

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Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0 x + 2 = 0ORx + 3 = 0 -2 -2 -3 -3 x = -2 OR x = -3

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Ex. 2 Solve x 2 = 6x by factoring.

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x 2 = 6x

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Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x

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Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0

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Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0

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Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0 x(x – 6) = 0

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Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0 x(x – 6) = 0 x = 0

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Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0 x(x – 6) = 0 x = 0

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Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0 x(x – 6) = 0 x = 0ORx – 6 = 0

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Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0 x(x – 6) = 0 x = 0ORx – 6 = 0 x = 0

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Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0 x(x – 6) = 0 x = 0ORx – 6 = 0 +6 +6 x = 0

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Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0 x(x – 6) = 0 x = 0ORx – 6 = 0 +6 +6 x = 0OR x = 6

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Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers.

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Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers. x = 4x = -5

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Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers. x = 4x = -5 -4 -4+5 +5

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Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers. x = 4x = -5 -4 -4+5 +5 x – 4 = 0 x + 5 = 0

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Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers. x = 4x = -5 -4 -4+5 +5 x – 4 = 0 x + 5 = 0 (x – 4)(x + 5) = 0

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Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers. x = 4x = -5 -4 -4+5 +5 x – 4 = 0 x + 5 = 0 (x – 4)(x + 5) = 0 x 2 + 5x – 4x – 20 = 0

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Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers. x = 4x = -5 -4 -4+5 +5 x – 4 = 0 x + 5 = 0 (x – 4)(x + 5) = 0 x 2 + 5x – 4x – 20 = 0 x 2 + x – 20 = 0

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