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Solving Quadratic Equations by Factoring - Download as PDF - PDF

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					Solving Quadratic Equations by Factoring
When presented with a quadratic equation (when the degree, or highest exponent, is 2), you are looking for
two solutions. In some special cases, there may be one solution or no real solutions. One method to solve
quadratic equations is to use factoring.

To solve for x, rearrange the equation so that one side says = 0. The other side should be written in standard
form. Factor it. For example:

                                               9 x 2 = −18 x − 8

                                              9 x 2 + 18 x + 8 = 0

                                             (3 x + 4)(3 x + 2) = 0

According to the ZERO-PRODUCT PROPERTY, if a factored equation equals zero then one of the factors
(3x + 4) or (3x + 2) must equal zero. Therefore, we can set each factor equal to zero and solve both resulting
equations to obtain the possible values of x.

                                        3x + 4 = 0           3x + 2 = 0

                                          3 x = −4           3 x = −2

                                                 4                    2
                                           x=−                x=−
                                                 3                    3


Solve each equation by factoring and using the zero-product property.

1. x 2 + 7 x = −10                                      2. x 2 = 2 x + 8




3. 27 − 12 x 2 = 0                                      4. x 2 + 35 x + 3 = 77
Solving Quadratic Equations by Factoring
Solve each equation by factoring and using the zero-product property.

1. x 2 − 5 x = 84                                     2. 4 x 2 − 21x + 5 = 0




3. x 2 + 5 x + 14 = 0                                 4. x ( x + 5) = 14




5. 2 x 2 − 17 x − 19 = 0                              6. x 2 + 3 x − 31 = −3




7. x 2 − 4 x = 0                                      8. −4 x 2 + 28 x = 0




9. 2 x 2 − 128 = 0                                    10. x 2 − 21x + 108 = 0
Solving Quadratic Equations by Factoring
Solve each equation by factoring and using the zero-product property.

1. x 2 − 9 x = −14                                    2. x 2 = 7 x




3. 2 x 2 − x = 1                                      4. x 2 + 10 x + 25 = 36




5. − x + x 2 = 56                                     6. 3 x 2 + 34 x + 11 = 0




7. x 2 − 11x = −18                                    8. 3 x 2 − 24 x + 48 = 0




9. 25 x 2 − 4 = 0                                     10. 2 x 2 = 3 − x
Solving Quadratic Equations by Factoring
Solve each equation by factoring and using the zero-product property.

1. 100 x 2 − 121 = 0                                  2. −2 x 2 − 4 x = 0




3. x 2 = x + 20                                       4. x 2 + 32 x = −220




5. 2 x 2 = 72                                         6. 10 x 2 + x − 10 = −2 x + 8




7. 5 x 2 − 2 x = 0                                    8. x 2 − 2 x − 3 = 0




9. x 2 + 26 x = −169                                  10. 5 x 2 + 11x + 2 = 0
Solving Quadratic Equations by Factoring
Solve each equation by factoring and using the zero-product property.

1. 2 x 2 + x = 0                                      2. 3 x 2 − 10 x − 8 = 0




3. 10 x + 16 = − x 2                                  4. 14 x 2 − 21x = 0




5. 4 x 2 + 64 = −32 x                                 6. 216 x 2 − 96 = 0




7. x 2 − 4 x − 5 = 0                                  8. 5 x 2 − 3 x − 26 = 0




9. − 4 x 2 − 4 x − 1 = 0
     5       5     5                                  10.   1
                                                            5   x2 − 2x + 5 = 0
Solving Quadratic Equations by Factoring
Solve each equation by factoring and using the zero-product property.

1. 2 x 2 + 3 x = 0                                    2. x 2 = 27 − 6 x




3. −3 x 2 − 2 x − 1 = 0
                  3                                   4. 50 x 2 + 60 x + 18 = 0




5. 4 x 2 − 36 = 0                                     6. x 2 + 30 = −13 x




7. 9 x 2 − 9 x = 28                                   8. x 2 − 19 x + 84 = 0




9. x ( x − 3) = 28                                    10. −3 x 2 − 9 x = 0

				
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posted:11/14/2011
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