factor 6x^2-48x+72 — step-by-step solution

⚠ 6x is read as the product 6*x: for a power, write 6^x

⚠ 48x is read as the product 48*x: for a power, write 48^x

Let's factorize in

ℝ

6 x^{2} - 48 x + 72

This expression can be factorized into:

6 \cdot (x^{2} - 8 x + 12)

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = {(-8)}^{2} - 4 \cdot 1 \cdot 12

Δ = 64 - 4 \cdot 12

Δ = 64 - 48

Δ = 16

Δ > 0

, the equation has two solutions:

The first solution is:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{8 - \sqrt{16}}{2}

x1 = \frac{8 - 4}{2}

x1 = \frac{4}{2}

x1 = 2

The second solution is:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{8 + \sqrt{16}}{2}

x2 = \frac{8 + 4}{2}

x2 = \frac{12}{2}

x2 = 6

Factors found:

(x - 2) \cdot (x - 6)

▶Factored expression:

6 \cdot (x - 2) \cdot (x - 6)