basic mathematics image
 basic mathematics image

factoring using the quadratic formula


Factoring using the quadratic formula is the goal of this lesson. It is closely related to solving equations using the quadratic formula

2 easy steps to follow when factoring using the quadratic formula:

Step #1:

Solve the quadratic equation to get x1 and x2

Step #2

Uisng the answers found in step #1, the factorization form is a (x - x1)(x - x2)


Example #1:


Factor 4x2 + 9x + 2 = 0 using the quadratic formula.

a = 4, b = 9, and c = 2

x = (-b ± √(b2 - 4ac)) / 2a

x = (-9 ± √(92 - 4 × 4 × 2)) / 2 × 4

x = (-9 ± √(81 - 4 × 4 × 2)) / 8

x = (-9 ± √(81 - 4 × 8)) / 8

x = (-9 ± √(81 - 32)) / 8

x = (-9 ± √(49)) / 8

x = (-9 ± 7 ) / 8

x1 = (-9 + 7 ) / 8

x1 = (-2 ) / 8

x1 = -1/4

x2 = (-9 - 7 ) / 8

x2 = (-16 ) / 8

x2 = -2


The factorization form is a (x - x1)(x - x2)

The factorization form is 4 (x - -1/4)(x - -2)

The factorization form is 4 (x + 1/4)(x + 2)

Now, use distributive property to simplify the expression by getting rid of fractions

4 (x + 1/4)(x + 2) = (4 × x + 4 × 1/4) (x + 2) = (4x + 1)(x + 2)


Example #2:


Factor x2 + 2x - 15 = 0 using the quadratic formula

a = 1, b = 2, and c = -15

x = (-b ± √(b2 - 4ac)) / 2a

x = (- 2 ± √(22  - 4 × 1 × -15)) / 2 × 1

x = (-2 ± √(4 - 4 × 1 × -15)) / 2

x = (-2 ± √(4 - 4 × -15)) / 2

x = (-2 ± √(4 + 60)) / 2

x = (-2 ± √(64)) / 2

x = (-2 ± 8 ) / 2

x1 = (-2 + 8 ) / 2

x1 = ( 6 ) / 2

x1 = 3

x2 = (-2 - 8 ) / 2

x2 = (-10) / 2

x2 = -5

The factorization form is a (x - x1)(x - x2)

The factorization form is 1 (x - 3)(x - -5)

The factorization form is 1 (x - 3)(x + 5)

Now, use distributive property to simplify the expression

1 (x - 3)(x + 5) = (1 × x + 1 × -3) (x + 2) = (x - 3)(x + 5)

It is important to understand how to use the quadratic formula before fatoring using the quadratic formula.






Page copy protected against web site content infringement by Copyscape





Bookmark and Share




Fractions-book-image












|Are you a fan of this site? Support us |Our awards! |Our partners |About me |Disclaimer |Build your website! |Advertise on my site |Try our free toolbar |Like us on Facebook |Take our survey|
Copyright © 2008. Basic-mathematics.com. All right reserved