Question

When a polynomial is divided by(x-1) the remainder is 5 and when it is divided by (x-2) the remainder is 7 find the remainder when it is divided by (x-1) (x-2)?

Answer 1

Answer:

Step-by-step explanation:

By remainder theorem, “When f(x) is divided by (x−1), the remainder is 5” can be translated to:-

(1) … f(1)=5

Similarly, we have:-

(2) … f(2)=7

When f(x) is divided by (x−1)(x−2), then basically we have:-

(3) … f(x)=(x−1)(x−2)Quotient + Remainder

Since the degree of the remainder must be one lower than that of the divisor, [=2 from (x−1)(x−2)]], the remainder can have degree = 1 (or lower) only. The remainder should then take the form ax+b, which is a general expression of degree 1 (or lower if a = 0) in x. Therefore, (3) becomes:-

(4) …f(x)=(x−1)(x−2)Q(x)+(ax+b)

(1) and (2) can be used to find the values of a and b from (4).