The area of a rectangle is open paren x to the 4th power plus 4 x cubed plus 3 x squared minus 4 x minus 4 close paren , and the length of the rectangle is open paren x cubed plus 5 x squared plus 8 x plus 4 close paren If area is equal to length times width , what is the width of the rectangle?

Width equals area divided by length. Dividing the leading terms gives x, and subtracting x(x³ + 5x² + 8x + 4) from the area leaves −x³ − 5x² − 8x − 4, which is −1 times the length. Thus the area is (x − 1)(x³ + 5x² + 8x + 4), so the width is x − 1, choice D.

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