Find the remainder when $x^{4} + 4 x^{3} - 5 x^{2} - 6 x + 7$ is divisible by $x - 3$ .

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Solution

We divide $x^{4} + 4 x^{3} - 5 x^{2} - 6 x + 7$ by $(x - 3)$ as shown in the above image:

From the division, we observe that the quotient is $x^{3} + 7 x^{2} + 16 x + 42$ and the remainder is $133$ .

Hence, the remainder is $133$ .

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