Using factors theorem, factories $x^{4} - x^{3} - 7 x^{3} + x + 6$

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Solution

factories $x^{4} - x^{3} - 7 x^{3} + x + 6$
$∴ x^{4} - x^{3} - 7 x^{3} + x + 6 = x^{3} (x - 1) - 7 x^{2} (x - 1) - 7 x (x - 1) - 6 (x - 1)$
$= (x - 1) (x^{3} - 7 x^{2} - 7 x - 6)$
$= (x - 1) (x - 2) (x^{2} + 4 x + 3)$
$= (x - 1) (x - 2) (x + 1) (x + 3)$

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