The area of a rectangle is (x4 + 4x3 + 3x2 – 4x – 4), and the length of the rectangle is (x3 + 5x2 + 8x + 4). If area = length × width, what is the width of the rectangle?

Since area = length × width, divide the area polynomial by the length polynomial. Testing x − 1 gives (x³ + 5x² + 8x + 4)(x − 1) = x⁴ + 4x³ + 3x² − 4x − 4, which matches the given area. So the width is x − 1, choice D.

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