(i) let p(x) = 69 + 11x −x² + x³ and g(x) = x + 3

We have to prove that g(x) is factor of p(x)

So the zero of g(x)= – 3

P( – 3) = 69 + 11( – 3) –( – 3)² + ( – 3) ³

= 69 – 69 = 0

Since the remainder is zero g(x) = x + 3 is factor of p(x)

(ii) Let p(x) = x + 2x³ – 9x² + 12 and g(x) =2x−3

We have to prove that g(x) is factor of p(x)

So the zero of g(x)= 3/2

Since the remainder is zero ∴ g(x) is factor of p(x)