About Solving Quadratic Equations by Factoring:
A quadratic equation in standard form: ax2 + bx + c = 0. a, b, & c are real numbers, & a ≠ 0. When the left side is factorable, we simply factor the left side and set each factor with a variable equal to zero. We then solve the resulting equations and check our results.
Test Objectives
- Demonstrate the ability to factor a polynomial
- Demonstrate the ability to use the zero product property
- Demonstrate the ability to check the proposed solutions for a quadratic equation
#1:
Instructions: Solve each quadratic equation by factoring.
a) v2 - 4v - 5 = 0
b) b2 - 2b + 1 = 0
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#2:
Instructions: Solve each quadratic equation by factoring.
a) v2 + 40 = 13v
b) k2 + 10 = -7k
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#3:
Instructions: Solve each quadratic equation by factoring.
a) 7x2 = 28x - 28
b) 5a2 = 15a
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#4:
Instructions: Solve each quadratic equation by factoring.
a) 6x2 + 23 = 19x + 8
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#5:
Instructions: Solve each quadratic equation by factoring.
a) 19x2 - 180x - 160 = -6x2
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Written Solutions:
#1:
Solutions:
a) v = 5 or v = -1
b) b = 1
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#2:
Solutions:
a) v = 8 or v = 5
b) k = -5 or k = - 2
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#3:
Solutions:
a) x = 2
b) a = 0 or a = 3
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#4:
Solutions:
a)
| x = | 3 | or | x = | 5 |
| 2 | 3 |
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#5:
Solutions:
a)
| x = | -4 | or | x = 8 |
| 5 |
