What is (x^3-7x+6)/(x-2) ?

The solution to (x^3-7x+6)/(x-2) is (x-1)(x+3)

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simplify (x^3-7x+6)/(x-2)

simplify

\frac{x ^{3} - 7 x + 6}{x - 2}

(x - 1) (x + 3)

Solution steps

\frac{x ^{3} - 7 x + 6}{x - 2}

Use the rational root theorem

= \frac{( x - 1 ) \frac{x ^{3} - 7 x + 6}{x - 1}}{x - 2}

\frac{x ^{3} - 7 x + 6}{x - 1} = x^{2} + x - 6

= \frac{( x - 1 ) ( x ^{2} + x - 6 )}{x - 2}

Factor

x^{2} + x - 6 : (x - 2) (x + 3)

= \frac{( x - 1 ) ( x - 2 ) ( x + 3 )}{x - 2}

Cancel the common factor:

x - 2

= (x - 1) (x + 3)

(- 6) + (- 3)

3 x - t - 2 x (x - t)

\frac{3}{6} \cdot \frac{2}{9}

\frac{8 ^{9}}{8 ^{3}}

4 \cdot \frac{3}{7}