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We know that the area of a rectangle is given by the formula A = lw, where A is the area, l is the length, and w is the width. We are given that the width is x+3 and the area is x^3 - 7x + 6. So we can set up the equation:
x^3 - 7x + 6 = (x+3)l
To solve for l, we can divide both sides by x+3:
l = (x^3 - 7x + 6) / (x+3)
Therefore, an expression for the length of the playground is (x^3 - 7x + 6) / (x+3).