5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.
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Transcript of 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.
![Page 1: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/1.jpg)
5.3 – Solving Quadratic Equations by Factoring
![Page 2: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/2.jpg)
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
![Page 3: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/3.jpg)
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
![Page 4: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/4.jpg)
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
![Page 5: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/5.jpg)
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
(x )(x ) = 0
![Page 6: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/6.jpg)
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
(x )(x ) = 0
(x + 2)(x + 3) = 0
![Page 7: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/7.jpg)
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
(x )(x ) = 0
(x + 2)(x + 3) = 0
![Page 8: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/8.jpg)
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
(x )(x ) = 0
(x + 2)(x + 3) = 0
x + 2 = 0
![Page 9: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/9.jpg)
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
(x )(x ) = 0
(x + 2)(x + 3) = 0
x + 2 = 0
![Page 10: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/10.jpg)
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
(x )(x ) = 0
(x + 2)(x + 3) = 0
x + 2 = 0 OR x + 3 = 0
![Page 11: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/11.jpg)
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
(x )(x ) = 0
(x + 2)(x + 3) = 0
x + 2 = 0 OR x + 3 = 0
-2 -2
![Page 12: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/12.jpg)
Ex. 1 Solve y = x2 + 5x + 6 by factoring. x2 + 5x + 6 = y x2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0x + 2 = 0 OR x + 3 = 0 -2 -2 x = -2
![Page 13: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/13.jpg)
Ex. 1 Solve y = x2 + 5x + 6 by factoring. x2 + 5x + 6 = y x2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0x + 2 = 0 OR x + 3 = 0 -2 -2 -3 -3 x = -2
![Page 14: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/14.jpg)
Ex. 1 Solve y = x2 + 5x + 6 by factoring. x2 + 5x + 6 = y x2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0x + 2 = 0 OR x + 3 = 0 -2 -2 -3 -3 x = -2 OR x = -3
![Page 15: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/15.jpg)
Ex. 2 Solve x2 = 6x by factoring.
![Page 16: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/16.jpg)
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
![Page 17: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/17.jpg)
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
![Page 18: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/18.jpg)
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
![Page 19: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/19.jpg)
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
![Page 20: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/20.jpg)
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
x(x – 6) = 0
![Page 21: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/21.jpg)
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
x(x – 6) = 0
x = 0
![Page 22: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/22.jpg)
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
x(x – 6) = 0
x = 0
![Page 23: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/23.jpg)
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
x(x – 6) = 0
x = 0 OR x – 6 = 0
![Page 24: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/24.jpg)
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
x(x – 6) = 0
x = 0 OR x – 6 = 0
x = 0
![Page 25: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/25.jpg)
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
x(x – 6) = 0
x = 0 OR x – 6 = 0
+6 +6
x = 0
![Page 26: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/26.jpg)
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
x(x – 6) = 0
x = 0 OR x – 6 = 0
+6 +6
x = 0 OR x = 6
![Page 27: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/27.jpg)
Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form
ax2 + bx + c = 0, where a, b, and c are integers.
![Page 28: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/28.jpg)
Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form
ax2 + bx + c = 0, where a, b, and c are integers.
x = 4 x = -5
![Page 29: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/29.jpg)
Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form
ax2 + bx + c = 0, where a, b, and c are integers.
x = 4 x = -5
-4 -4 +5 +5
![Page 30: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/30.jpg)
Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form
ax2 + bx + c = 0, where a, b, and c are integers.
x = 4 x = -5
-4 -4 +5 +5
x – 4 = 0 x + 5 = 0
![Page 31: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/31.jpg)
Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form
ax2 + bx + c = 0, where a, b, and c are integers.
x = 4 x = -5
-4 -4 +5 +5
x – 4 = 0 x + 5 = 0
(x – 4)(x + 5) = 0
![Page 32: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/32.jpg)
Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form
ax2 + bx + c = 0, where a, b, and c are integers.
x = 4 x = -5
-4 -4 +5 +5
x – 4 = 0 x + 5 = 0
(x – 4)(x + 5) = 0
x2 + 5x – 4x – 20 = 0
![Page 33: 5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfaf1a28abf838c9d16e/html5/thumbnails/33.jpg)
Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form
ax2 + bx + c = 0, where a, b, and c are integers.
x = 4 x = -5
-4 -4 +5 +5
x – 4 = 0 x + 5 = 0
(x – 4)(x + 5) = 0
x2 + 5x – 4x – 20 = 0
x2 + x – 20 = 0