Find the remainder when $x^{4} + 2 x^{3} - 13 x^{2} - 14 x + 24$ is divisible by $(x - 1)$ .

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Solution

Let $f (x) =$ $x^{4} + 2 x^{3} - 13 x^{2} - 14 x + 24$ .

Here, $f (x)$ is divided by $(x - 1)$ .

According to the remainder theorem, we have when $f (x)$ is divisible by $(x - 1)$ , then the remainder is $f (1)$ .

Now, $f (1) = 1 + 2 - 13 - 14 + 24 = 0$ .

So, $f (x)$ is perfectly divisible by $(x - 1)$
and the remainder obtained is $0$ .

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Find the remainder when x4+2x3−13x2−14x+24 is divisible by (x−1).

Let f(x)=x4+2x3−13x2−14x+24.Here, f(x) is divided by (x−1).According to the remainder theorem, we have when f(x) is divisible by (x−1), then the remainder is f(1).Now, f(1)=1+2−13−14+24=0.So, f(x) is perfectly divisible by (x−1)and the remainder obtained is 0.

Find the remainder when $x^{4} + 2 x^{3} - 13 x^{2} - 14 x + 24$ is divisible by $(x - 1)$ .