x⁴ − 7x³+ 9x² + 7x − 10

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Solution

Let be the given polynomial.

Now, putting we get

$f (1) = {(1)}^{4} - 7 {(1)}^{3} + 9 {(1)}^{2} + 7 (1) - 10 = 1 - 7 + 9 + 7 - 10 = 0$

Therefore, is a factor of polynomial f(x).

Now,
$f (x) = x^{4} - x^{3} - 6 x^{3} + 6 x^{2} + 3 x^{2} - 3 x + 10 x - 10$

Where

Putting we get

Therefore, is a factor of g(x).

Now,
$g (x) = x^{3} - 7 x^{2} + x^{2} - 7 x + 10 x + 10$

From equation (i) and (ii), we get

Hence are the factors of polynomial f(x).

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