Question

A number is to be divided by 1001 (= 7x11x13) and it was divided in
02
the remainders 4, 6 and 12 respectively. What would have been the sanded
directly by 1001?
970
O2
982
828
764​

Answer 1

Answer:

Answer : The answer will be 970

Answer 2

970 is the remainder.

• When a polynomial is divided by a linear polynomial, the remainder theorem is used to get the remaining. Long division of polynomials can be used to find the remainder after dividing one polynomial by another. The remainder can instead be discovered using the remainder theorem.
• The remainder theorem states that when a linear polynomial q(x) with a zero of x = a divides a polynomial p(x) (whose degree is greater than or equal to 1), the remainder is given by r = p. (a).

Here according to the given information, we are given that,

A number when divided by 1001 that is $7.11.13$, we get the remainders as 4, 6 and 12 respectively.

Now, by remainder theorem, we get,

$13.1+12 = 25.\\25.11+6 = 281.\\281.7+4 = 1971.$

This means that the number is 1971.

In order to get the remainder when 1971 is divided by 1001, we get,

$1000.1+970 = 1971.$

Hence, 970 is the remainder.

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