What is (3x^3-4x^2-5x+2)/(x-2) ?

The solution to (3x^3-4x^2-5x+2)/(x-2) is (x+1)(3x-1)

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simplify (3x^3-4x^2-5x+2)/(x-2)

simplify

\frac{3 x ^{3} - 4 x ^{2} - 5 x + 2}{x - 2}

(x + 1) (3 x - 1)

Solution steps

\frac{3 x ^{3} - 4 x ^{2} - 5 x + 2}{x - 2}

Use the rational root theorem

= \frac{( x + 1 ) \frac{3 x ^{3} - 4 x ^{2} - 5 x + 2}{x + 1}}{x - 2}

\frac{3 x ^{3} - 4 x ^{2} - 5 x + 2}{x + 1} = 3 x^{2} - 7 x + 2

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

Factor

3 x^{2} - 7 x + 2 : (3 x - 1) (x - 2)

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

Cancel the common factor:

x - 2

= (x + 1) (3 x - 1)

x \cdot (x + 1)

4 x^{2} + 20 x

+ 4 - 1

(5 p + 2)^{2}

+ 6 - 3

What is (3x^3-4x^2-5x+2)/(x-2) ?
The solution to (3x^3-4x^2-5x+2)/(x-2) is (x+1)(3x-1)