What is (x^3+x^2-10x+8)/(x-2) ?

The solution to (x^3+x^2-10x+8)/(x-2) is (x-1)(x+4)

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simplify (x^3+x^2-10x+8)/(x-2)

simplify

\frac{x ^{3} + x ^{2} - 10 x + 8}{x - 2}

(x - 1) (x + 4)

Solution steps

\frac{x ^{3} + x ^{2} - 10 x + 8}{x - 2}

Use the rational root theorem

= \frac{( x - 1 ) \frac{x ^{3} + x ^{2} - 10 x + 8}{x - 1}}{x - 2}

\frac{x ^{3} + x ^{2} - 10 x + 8}{x - 1} = x^{2} + 2 x - 8

= \frac{( x - 1 ) ( x ^{2} + 2 x - 8 )}{x - 2}

Factor

x^{2} + 2 x - 8 : (x - 2) (x + 4)

= \frac{( x - 1 ) ( x - 2 ) ( x + 4 )}{x - 2}

Cancel the common factor:

x - 2

= (x - 1) (x + 4)

\frac{5}{3} - \frac{2}{3}

x^{3} x^{- 4} y^{0}

\frac{x ^{2} + 6 x + 8}{x ^{2} + 5 x + 4}

(x - 1) (x^{2} - 2 x + 1)

\frac{x ^{2} - 9}{x ^{4} - 81}

What is (x^3+x^2-10x+8)/(x-2) ?
The solution to (x^3+x^2-10x+8)/(x-2) is (x-1)(x+4)