What is (x^3-2x^2-5x+6)/(x-3) ?

The solution to (x^3-2x^2-5x+6)/(x-3) is (x-1)(x+2)

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simplify (x^3-2x^2-5x+6)/(x-3)

simplify

\frac{x ^{3} - 2 x ^{2} - 5 x + 6}{x - 3}

(x - 1) (x + 2)

Solution steps

\frac{x ^{3} - 2 x ^{2} - 5 x + 6}{x - 3}

Use the rational root theorem

= \frac{( x - 1 ) \frac{x ^{3} - 2 x ^{2} - 5 x + 6}{x - 1}}{x - 3}

\frac{x ^{3} - 2 x ^{2} - 5 x + 6}{x - 1} = x^{2} - x - 6

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

Factor

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

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

Cancel the common factor:

x - 3

= (x - 1) (x + 2)

20 \cdot 7

(\frac{3}{3} + \frac{5}{2} i)^{2}

4 x^{3} - 5 x^{2} + 64 x - 80

5 \times 1 0^{- 4}

\frac{12 a ^{3} b ^{2} c - 18 a ^{4} b ^{5} c ^{2}}{6 a ^{2} b c}

What is (x^3-2x^2-5x+6)/(x-3) ?
The solution to (x^3-2x^2-5x+6)/(x-3) is (x-1)(x+2)