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

Recent Articles

  1. Average age word problem

    Aug 09, 16 01:40 PM

    Average age of Dipu and Apu is 22 years. Average age of Dipu and Tipu is 24 years. Age of Dipu is 21 years. What are the ages of Apu, and tipu ? Let

    Read More



New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.