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Find the remainder when $x 3 + 3 x 2 + 3 x + 1$ is divided by $x − 12$ .

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274

298

278

18

answer is C.

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Detailed Solution

We assume the given polynomial as p(x).
So, we write the given expressions as

x − 12

and

p (x) = x 3 + 3 x 2 + 3 x + 1

.
We have to find the remainder when

x − 12

is the divisor of the polynomial p(x).
Therefore, in line with the above let us find out the zero of the divisors by equating it to zero.

x − 12 = 0 x = 12

We now get the remainder by putting the zero of the divisors in the polynomial p(x) in the following way.

p (x) x = 12 = x 3 + 3 x 2 + 3 x + 1 x = 12 = 123 + 3 × 122 + 3 × 12 + 1 = 18 + 34 + 32 + 1 = 1 + 6 + 12 + 8 8 = 278

Thus, we can now conclude that the remainder when

x 3 + 3 x 2 + 3 x + 1

is divided by

x − 12

278

.
Therefore, the correct option is 3.

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