What is (2x^3-5x^2-9x+18)/(x+2) ?

The solution to (2x^3-5x^2-9x+18)/(x+2) is (2x-3)(x-3)

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simplify (2x^3-5x^2-9x+18)/(x+2)

simplify

\frac{2 x ^{3} - 5 x ^{2} - 9 x + 18}{x + 2}

(2 x - 3) (x - 3)

Solution steps

\frac{2 x ^{3} - 5 x ^{2} - 9 x + 18}{x + 2}

Use the rational root theorem

= \frac{( x + 2 ) \frac{2 x ^{3} - 5 x ^{2} - 9 x + 18}{x + 2}}{x + 2}

\frac{2 x ^{3} - 5 x ^{2} - 9 x + 18}{x + 2} = 2 x^{2} - 9 x + 9

= \frac{( x + 2 ) ( 2 x ^{2} - 9 x + 9 )}{x + 2}

Factor

2 x^{2} - 9 x + 9 : (2 x - 3) (x - 3)

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

Cancel the common factor:

x + 2

= (2 x - 3) (x - 3)

- x^{2} 48 x^{3} - 8 x 12 x^{5}

\frac{1}{1 + i}

\frac{x ^{- 4}}{x ^{3}}

19 \times 7

8 x^{2} - 18 x + 7

What is (2x^3-5x^2-9x+18)/(x+2) ?
The solution to (2x^3-5x^2-9x+18)/(x+2) is (2x-3)(x-3)