What is (2x^3-3x^2-23x+12)/(x+3) ?

The solution to (2x^3-3x^2-23x+12)/(x+3) is (2x-1)(x-4)

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simplify (2x^3-3x^2-23x+12)/(x+3)

simplify

\frac{2 x ^{3} - 3 x ^{2} - 23 x + 12}{x + 3}

(2 x - 1) (x - 4)

Solution steps

\frac{2 x ^{3} - 3 x ^{2} - 23 x + 12}{x + 3}

Use the rational root theorem

= \frac{( 2 x - 1 ) \frac{2 x ^{3} - 3 x ^{2} - 23 x + 12}{2 x - 1}}{x + 3}

\frac{2 x ^{3} - 3 x ^{2} - 23 x + 12}{2 x - 1} = x^{2} - x - 12

= \frac{( 2 x - 1 ) ( x ^{2} - x - 12 )}{x + 3}

Factor

x^{2} - x - 12 : (x + 3) (x - 4)

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

Cancel the common factor:

x + 3

= (2 x - 1) (x - 4)

2 \times \frac{4}{5}

\frac{28}{32}

3 \frac{1}{16}

121 - 64 x^{2}

\frac{4 + 3 i}{3 - 4 i}

What is (2x^3-3x^2-23x+12)/(x+3) ?
The solution to (2x^3-3x^2-23x+12)/(x+3) is (2x-1)(x-4)