What is (2x^3+x^2-17x+14)/(2x+7) ?

The solution to (2x^3+x^2-17x+14)/(2x+7) is (x-1)(x-2)

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simplify (2x^3+x^2-17x+14)/(2x+7)

simplify

\frac{2 x ^{3} + x ^{2} - 17 x + 14}{2 x + 7}

(x - 1) (x - 2)

Solution steps

\frac{2 x ^{3} + x ^{2} - 17 x + 14}{2 x + 7}

Use the rational root theorem

= \frac{( x - 1 ) \frac{2 x ^{3} + x ^{2} - 17 x + 14}{x - 1}}{2 x + 7}

\frac{2 x ^{3} + x ^{2} - 17 x + 14}{x - 1} = 2 x^{2} + 3 x - 14

= \frac{( x - 1 ) ( 2 x ^{2} + 3 x - 14 )}{2 x + 7}

Factor

2 x^{2} + 3 x - 14 : (x - 2) (2 x + 7)

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

Cancel the common factor:

2 x + 7

= (x - 1) (x - 2)

6 - \frac{10}{3}

\frac{7}{3 3}

\frac{1}{2 \times 7 \times π}

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

0. 5^{\frac{2}{3}}

What is (2x^3+x^2-17x+14)/(2x+7) ?
The solution to (2x^3+x^2-17x+14)/(2x+7) is (x-1)(x-2)