What should be subtracted to the polynomial x^{2} – 16x + 30, so that 15 is the zero of the resulting polynomial?

Given,

p(x) = x^{2} – 16x + 30

15 is the zero of the resulting polynomial,

So we get;

p(15) = (15)^{2} – 16 × 15 + 30

p(15) = 225 – 240 + 30

p(15) = 15

∴ 15 should be subtracted from the given polynomial to get 15 as the zero of the resulting polynomial.

We can also verify the answer;

By adding 2 to the given polynomial we get;

P(x) = x^{2} – 16x + 30 – 15

P(x) = x^{2} – 16x + 15

P(15) = 225 – 240 + 15

P(15) = 240 – 240

P(15) = 0

Hence proved that 15 is the right answer to get 15 as the zero of resulting polynomial.

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