Question

problem 4 factoring a polynomial model got it? in problem 4, suppose the side length of the square is 6x and the radius of the circle is 3x. what is the factored form of the area of the shaded region?

Explanation:

Step1: Find area of square

The area of a square is side squared. The side length is \(6x\), so area of square is \((6x)^2 = 36x^2\).

Step2: Find area of circle

The area of a circle is \(\pi r^2\). The radius \(r = 3x\), so area of circle is \(\pi(3x)^2=\pi\times9x^2 = 9\pi x^2\).

Step3: Find area of shaded region (assuming shaded is square minus circle)

Subtract area of circle from area of square: \(36x^2-9\pi x^2\). Factor out the common term \(9x^2\): \(9x^2(4 - \pi)\).

Answer:

\(9x^2(4 - \pi)\)