factorize x^2-3x-4 — step-by-step solution

Let's factor in

ℝ

x^{2} - 3 x - 4

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = {(-3)}^{2} - 4 \cdot 1 \cdot -4

Δ = 9 - 4 \cdot -4

Δ = 9 + 16

Δ = 25

Since

Δ > 0

, the equation has two solutions:

For the 1st solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{3 - \sqrt{25}}{2}

x1 = \frac{3 - 5}{2}

x1 = - \frac{2}{2}

x1 = -1

For the 2nd solution, we obtain:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{3 + \sqrt{25}}{2}

x2 = \frac{3 + 5}{2}

x2 = \frac{8}{2}

x2 = 4

▷Result: $(x + 1) \cdot (x - 4)$