factor 4x^2-8x+16 — step-by-step solution

Let's factor in

ℝ

4 x^{2} - 8 x + 16

We factor out

4

, the greatest common divisor of the coefficients:

4 x^{2} - 8 x + 16

4 \cdot (x^{2} - 2 x + 4)

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

. Here

a = 1

b = -2

and

c = 4

Δ = {(-2)}^{2} - 4 \cdot 1 \cdot 4

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

{(-2)}^{2}

(-2) \cdot (-2)

4

Δ = 4 - 4 \cdot 4

ⓘ Multiplications are done before additions and subtractions:

4 \cdot 4

16

Δ = 4 - 16

ⓘ Start from

4

and move back

16

on the number line, going below zero:

4 - 16

-12

Δ = -12

Δ < 0

, the equation has no real root.

Factor found:

x^{2} - 2 x + 4

▶Factored expression:

4 \cdot (x^{2} - 2 x + 4)