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

Let's factor in

ℝ

x^{2} + x - 2

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = 1 - 4 \cdot 1 \cdot -2

Δ = 1 - 4 \cdot -2

Δ = 1 + 8

Δ = 9

Δ > 0

, the equation has two solutions:

For the first solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{- 1 - \sqrt{9}}{2}

x1 = - \frac{1 + 3}{2}

x1 = - \frac{4}{2}

x1 = -2

Solution second:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{- 1 + \sqrt{9}}{2}

x2 = \frac{- 1 + 3}{2}

x2 = \frac{2}{2}

x2 = 1

▷Answer: $(x + 2) \cdot (x - 1)$