factorize x^2-x-6 — step-by-step solution

Let's factor in

ℝ

x^{2} - x - 6

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = {(-1)}^{2} - 4 \cdot 1 \cdot -6

Δ = 1 - 4 \cdot -6

Δ = 1 + 24

Δ = 25

Δ > 0

, the equation has two solutions:

Solution 1st:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{1 - \sqrt{25}}{2}

x1 = \frac{1 - 5}{2}

x1 = - \frac{4}{2}

x1 = -2

For the 2nd solution, we obtain:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{1 + \sqrt{25}}{2}

x2 = \frac{1 + 5}{2}

x2 = \frac{6}{2}

x2 = 3

▷Answer: $(x + 2) \cdot (x - 3)$