﻿ GreeneMath.com - Solving Quadratic Equations by Factoring Test

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 Test:

#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:

Solution:

a) v = 5 or v = -1

b) b = 1

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#2:

Solution:

a) v = 8 or v = 5

b) k = -5 or k = - 2

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#3:

Solution:

a) x = 2

b) a = 0 or a = 3

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#4:

Solution:

a)

 x = 3 or x = 5 2 3

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#5:

Solution:

a)

 x = -4 or x = 8 5

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