The are of a square can be represented by the polynomial 4x^2-16x+16. Find the length of a side of the square in terms of x.

(2x-4)(2x-4) is that polynomial factored

so each side must be 2x-4

To find the length of a side of the square in terms of x, we need to find the square root of the polynomial 4x^2 - 16x + 16.

Step 1: Calculate the square root
To find the square root, we need to factor the polynomial, if possible.

The given polynomial, 4x^2 - 16x + 16, is a perfect square trinomial since the first and third terms are perfect squares, and the middle term is twice the product of the square roots of the first and third terms.

When we factor this polynomial, we get:
4x^2 - 16x + 16 = (2x - 4)^2

Step 2: Take the square root
To find the square root, we take the square root of both sides of the equation:
√(4x^2 - 16x + 16) = √((2x - 4)^2)

Simplifying this expression gives us:
√(4x^2 - 16x + 16) = 2x - 4

So, the length of a side of the square in terms of x is 2x - 4.