State the reminder theoram
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Yogita Ingle 4 years, 1 month ago
Remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a).
Proof: Let p(x) be any polynomial with degree greater than or equal to 1. Suppose that when p(x) is divided by x – a, the quotient is q(x) and the remainder is r(x), i.e., p(x) = (x – a) q(x) + r(x) -- (i)
Since the degree of x – a is 1 and the degree of r(x) is less than the degree of x – a, the degree of r(x) = 0. This means that r(x) is a constant, say r. Thus we can re-write eq (i) as p(x) = (x – a) q(x) + r –(ii)
In particular, if x = a, then eq (ii) becomes p(a) = (a – a) q(a) + r = r,
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