What should be subtracted from the polynomial x2 - 16x + 30 so that the resulting polynomial will have a root 15;

Concept Used:

If any polynomial p(x) has a root x = a, then p(a) = 0.

Explanation:

We have the polynomial x2 - 16x + 30 

Let c be the value which needed to be subtracted from the polynomial.

⇒ x² - 16x + 30 - c has a root of 15.

If a polynomial has a root at x = 15, it means that when you substitute x = 15 into the polynomial, the result should be equal to zero. 

⇒ 15² - 16 ⋅ 15 + 30 - c = 0

⇒ 225 - 240 + 30 - c = 0

⇒ 15 - c = 0

⇒ c = 15

So, you should subtract 15 from the polynomial x² - 16x + 30 to make it have a root of 15.