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
Solving Quadratic Equations by Factoring Practice Test:

#1:

Instructions: Solve each quadratic equation by factoring.

a) v2 - 4v - 5 = 0

b) b2 - 2b + 1 = 0


#2:

Instructions: Solve each quadratic equation by factoring.

a) v2 + 40 = 13v

b) k2 + 10 = -7k


#3:

Instructions: Solve each quadratic equation by factoring.

a) 7x2 = 28x - 28

b) 5a2 = 15a


#4:

Instructions: Solve each quadratic equation by factoring.

a) 6x2 + 23 = 19x + 8


#5:

Instructions: Solve each quadratic equation by factoring.

a) 19x2 - 180x - 160 = -6x2


Written Solutions:

#1:

Solutions:

a) v = 5 or v = -1

b) b = 1


#2:

Solutions:

a) v = 8 or v = 5

b) k = -5 or k = - 2


#3:

Solutions:

a) x = 2

b) a = 0 or a = 3


#4:

Solutions:

a)

x =  3  or  x =  5
2 3

#5:

Solutions:

a)

x =  -4  or  x = 8
 5