# If the polynomial ax^{3} + bx^{2} - c is divisible by x^{2} + bx +c then what is the value of 'ab'?

A polynomial is a type of expression in which the exponents of all variables should be a whole number.

## Answer: If the polynomial ax^{3} + bx^{2} - c is divisible by x^{2} + bx + c then value of ab is 1.

As ax^{3} + bx^{2} - c is divisible by x^{2} + bx +c, then the remainder is 0.

**Explanation:**

The remainder when ax^{3} + bx^{2} - c is divided by x^{2} + bx +c is 0.

Let f(x) = ax^{3} + bx^{2} - c and g(x) = x^{2} + bx + c

Now, dividing f(x) by g(x) we get, (ax^{3} +bx^{2} - c) / (x^{2} + bx + c)

Use the Cuemath's long division of polynomial calculator, to find the quotient and the remainder.

We see that the quotient comes to be (ax - ab) and the remainder = (ab² – ac + b) x + c (ab – 1)

Now as the remainder is 0 and the value of x and c is not equal to 0.

Therefore, ab² – ac + b = 0 and ab – 1 = 0

==> ab = 1