Question

If the polynomial (x⁴ + 2x³ + 8x² + 12x + 18) is divided by another polynomial (x² + 5), the remainder comes out to be (px + q). Find values of p and q.

Answer 1

Let f(x) = (x⁴ + 2x³ + 8x² + 12x + 18) and g(x) = (x² + 5)

On dividing f(x) by g(x), we get

Now, px + q = 2x + 3 ⇒ p = 2, q = 3 (By comparing the coefficient of x and constant term)