The area of a rectangle is open paren x cubed minus 5 x squared plus 3 x minus 15 close paren , and the width of the rectangle is open paren x squared plus 3 close paren If area is equal to length times width , what is the length of the rectangle?

Since area = length × width, divide the area by the width. Factor the area by grouping: x³ − 5x² + 3x − 15 = x²(x − 5) + 3(x − 5) = (x² + 3)(x − 5). Dividing by the width, x² + 3, leaves x − 5, so the length is x minus 5.

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