Find the values of a and b if the following polynomials are perfect squares.

a x⁴–bx³ + 40 x² + 24x + 36

Step 1: Find the algebraic expression whose square gives the first term.

Step 2: Add the divisor and quotient .To this sum add a suitable expression and add the same expression in the quotient such that the product gives the next term.

Step 3: Continue the process until all the terms are divided.

We rearrange the equation in the increasing order of power of x.

The polynomial becomes 36 + 24x + 40x²–bx³ + ax⁴

Since it is a perfect square the remainder is 0

a = 9, b = –12