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

A and B each have certain number of oranges. A says to B if you give me 10 of your oranges, I will have twice the number of oranges left with you. B replies if you give me 10 of your oranges then I will have the same number of oranges as left with you. Find the number of oranges with a and b.

If the product of zeroes of the polynomial ax² – 6x – 6 is 4. Find the value of “a”.

Find a quadratic polynomial whose zeros are 2 + √3 and 2 – √3.

(x² – 2x + k) the remainder comes out to be (x + a). Find k and a.

If one zero of the polynomial 3x² – 8x + 2k + 1 is seven times of other then, Find the value of k.