In 2000 B.C., the Babylonians solved polynomial equations by referring to tables of values. One such table gave the values of y3 + y2. To be able to use this table, the Babylonians sometimes used the method below to manipulate the equation.

Then they would find (a2c)/b3 in the y3 + y2 column of the table. They knew that the corresponding y-value was equal to (ax)/b, so they could conclude that x = (by)/a.
(a) Calculate y3 + y2 for y = 1, 2, 3, . . . , 10. Record the values in a table.
(b) Use the table from part (a) and the method above to solve each equation.
(i) x3 + x2 = 252
(ii) x3 + 2x2 = 288
(iii) 3x3 + x2 = 90
(iv) 2x3 + 5x2 = 2500
(v) 7x3 + 6x2 = 1728
(vi) 10x3 + 3x2 = 297

ax3 + bx? = c Original equation %3D a'x b3 ac a?x? Multiply each side by b2 a?c ax Rewrite.