Both (x – 2) and are factors of the polynomial px² + 5x + r, let us calculate and write the relation between p and r.

The given polynomial is px² + 5x + r.

Given that, (x – 2) is the factor of the polynomial, we have f(2) = 0.

So, f(2) = p(2)² + 5(2) + r = 0

4p + 10 + r = 0 ……… (1)

Now, given that, is the factor of the polynomial, we have

So,

From (1), we get r = -4p – 10

So, we can say that the relation between p and r is r = -4p – 10.

⸫ the relation between p and r is r = -4p – 10.