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Polynomial and Its General Form

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Question

Check whether the polynomial $6 x^{4} + 8 x^{3} - 5 x^{2} - 6 x - 3$ is exactly divisible by the polynomial $x - 1$ .

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Solution

Let $f (x) =$ $6 x^{4} + 8 x^{3} - 5 x^{2} - 6 x - 3$ .
Now $f (1) = 6 + 8 - 5 - 6 - 3 = 0$ .
Then by remainder theorem we have $f (x)$ is exactly divisible by $(x - 1)$ >

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