Question

what should be added to 15232 so that it is exactly divisible by 65​

Answer 1

Answer:

Solution -

Divide the number 3485 by 65,

3485=65\times 53 + 403485 = 65 × 53 + 40

Take one more multiple of 65 i.e. 54

So, if we multiply 65 by 54 and subtract from given number we get the required number.

65\times 54 = 351065 × 54 = 3510

Subtract,

3510 - 3485 = 253510 − 3485 = 25

The required smallest number that should be added to 3485 so that it is exactly divisible by 65 is 25.

Answer 2

Answer:

It is given that the dividend is p(x)=x

4

−1, the divisor is g(x)=x

2

+2x+1, therefore, the division is as shown above.

Therefore, from the division, we get that the remainder is r(x)=(−4x−4) that is −r(x)=4x+4.

Hence, 4x+4 should be added to x

4

−1 so that the resulting polynomial is exactly divisible by x

2

+2x+1.