factorize x^2+5x+6 — step-by-step solution

Let's factor in

ℝ

x^{2} + 5 x + 6

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = 5^{2} - 4 \cdot 1 \cdot 6

Δ = 25 - 4 \cdot 6

Δ = 25 - 24

Δ = 1

Δ > 0

, the equation has two solutions:

For the 1st solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

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

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

x1 = - \frac{6}{2}

x1 = -3

For the 2nd solution, we obtain:

\frac{- b + \sqrt{Δ}}{2 a}

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

x2 = - \frac{4}{2}

x2 = -2

▷Answer: $(x + 2) \cdot (x + 3)$