A quadratic equation in standard form: ax^{2} + 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
Solving Quadratic Equations by Factoring Test:
#1:
Instructions: Solve each quadratic equation by factoring.
a) v^{2} - 4v - 5 = 0
b) b^{2} - 2b + 1 = 0
#2:
Instructions: Solve each quadratic equation by factoring.
a) v^{2} + 40 = 13v
b) k^{2} + 10 = -7k
#3:
Instructions: Solve each quadratic equation by factoring.
a) 7x^{2} = 28x - 28
b) 5a^{2} = 15a
#4:
Instructions: Solve each quadratic equation by factoring.
a) 6x^{2} + 23 = 19x + 8
#5:
Instructions: Solve each quadratic equation by factoring.
a) 19x^{2} - 180x - 160 = -6x^{2}
Written Solutions:
Solution:
a) v = 5 or v = -1
b) b = 1
Solution:
a) v = 8 or v = 5
b) k = -5 or k = - 2
Solution:
a) x = 2
b) a = 0 or a = 3
Solution:
a)
x = | 3 | or | x = | 5 |
2 | 3 |
Solution:
a)
x = | -4 | or | x = 8 |
5 |