### About Solving Quadratic Equations by Factoring:

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

#1:

Instructions: Solve each quadratic equation by factoring.

a) v^{2} - 4v - 5 = 0

b) b^{2} - 2b + 1 = 0

Watch the Step by Step Video Solution View the Written Solution

#2:

Instructions: Solve each quadratic equation by factoring.

a) v^{2} + 40 = 13v

b) k^{2} + 10 = -7k

Watch the Step by Step Video Solution View the Written Solution

#3:

Instructions: Solve each quadratic equation by factoring.

a) 7x^{2} = 28x - 28

b) 5a^{2} = 15a

Watch the Step by Step Video Solution View the Written Solution

#4:

Instructions: Solve each quadratic equation by factoring.

a) 6x^{2} + 23 = 19x + 8

Watch the Step by Step Video Solution View the Written Solution

#5:

Instructions: Solve each quadratic equation by factoring.

a) 19x^{2} - 180x - 160 = -6x^{2}

Watch the Step by Step Video Solution View the Written Solution

Written Solutions:

#1:

Solutions:

a) v = 5 or v = -1

b) b = 1

Watch the Step by Step Video Solution

#2:

Solutions:

a) v = 8 or v = 5

b) k = -5 or k = - 2

Watch the Step by Step Video Solution

#3:

Solutions:

a) x = 2

b) a = 0 or a = 3

Watch the Step by Step Video Solution

#4:

Solutions:

a)

x = | 3 | or | x = | 5 |

2 | 3 |

Watch the Step by Step Video Solution

#5:

Solutions:

a)

x = | -4 | or | x = 8 |

5 |