f(x) = 4x⁴ − 3x³ − 2x² + x − 7, g(x) = x − 1

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Solution

Let us denote the given polynomials as

We have to find the remainder whenis divided by.

By the remainder theorem, whenis divided bythe remainder is

Now we will show remainder by actual division

So the remainder by actual division is −7

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Similar questions

In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division.

f(x) = $4 x^{4} - 3 x^{3} - 2 x^{2} + x - 7$ , g(x) = x - 1

4 x^{4} - 3 x^{3} - 2 x^{2} + 6 x - 7

x - 2

x + 2 x^{2} + 3 x^{3} + 4 x^{4} + . . . . . .

[(4 x^{4} - 3 x^{3} - 2 x^{2} + 4 x - 3)

(x - 1)

The remainder when $4 x^{4} - 3 x^{3} + 2 x^{2} - x$ is divided by $x + 1$ is ___.

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