factor 2x^2-8x-42 — step-by-step solution

Let's factor in

ℝ

2 x^{2} - 8 x - 42

This expression can be factorized into:

2 \cdot (x^{2} - 4 x - 21)

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = {(-4)}^{2} - 4 \cdot 1 \cdot (-21)

Δ = 16 - 4 \cdot (-21)

Δ = 16 + 84

Δ = 100

Since

Δ > 0

, the equation has two solutions:

For the first solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{4 - \sqrt{100}}{2}

x1 = \frac{4 - 10}{2}

x1 = - \frac{6}{2}

x1 = -3

The second solution is:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{4 + \sqrt{100}}{2}

x2 = \frac{4 + 10}{2}

x2 = \frac{14}{2}

x2 = 7

Factors found:

(x + 3) \cdot (x - 7)

▶Factored expression:

2 \cdot (x + 3) \cdot (x - 7)