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

Step # 1:

Solve the quadratic equation for x 1 and x 2

Step # 2

Use the answers found in step # 1, the form of factoring is a (x – x 1) (x – x 2)

Example # 1:

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

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

x = (BC ± v (b2 – 4ac)) / 2

x = (-9 ± v (92-4 × 4 × 2)) / 2 × 4

x = (-9 ± v (81-4 × 4 × 2)) / 8

x = (-9 ± v (81-4 × 8)) / 8

x = (-9 ± v(81-32)) / 8

x = (-9 ± v (49)) / 8

x = (-9 ± 7) / 8

x 1 = (-9 + 7) / 8

x 1 = (-2) / 8

x 1 =-1/4

x 2 = (-9-7) / 8

x 2 =-(16) / 8

x 2 = – 2

The factorization is a (x – x 1) (x – x 2)

The factorization is 4 (x – 1/4) (x – 2)

The factorization is 4 (x + 1/4)(x_+_2)

Now, to 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) = (4 x + 1) (x + 2)

Example # 2:

Factor x 2 + 2 x – 15 = 0, using the quadratic formula

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

x = (BC ± v (b2 – 4ac)) / 2

x = (-2 ± v (22-4 × 1-15)) / 2 × 1

x = (-2 ± v (4-4 × 1-15)) / 2

x = (-2 ± v (× 4-4-15)) / 2

x = (-2 ± v (4 + 60)) / 2

x = (2 ± v (64)) / 2

x = (-2 ± 8) / 2

x 1 = (-2 + 8) / 2

x 1 = (6) / 2

x 1 = 3.

x 2 = (-2-8) / 2

x 2 = (-10) / 2

x 2 = – 5

The factorization is a (x – x 1) (x – x 2)

The factorization is 1 (x – 3) (x – 5)

The factorization is 1 (x – 3) (x + 5)

Now, use the 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 front of fatoring using the quadratic formula.