What is (12x^3+13x^2-59x+30)/(4x-5) ?

The solution to (12x^3+13x^2-59x+30)/(4x-5) is (x+3)(3x-2)

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simplify (12x^3+13x^2-59x+30)/(4x-5)

simplify

\frac{12 x ^{3} + 13 x ^{2} - 59 x + 30}{4 x - 5}

(x + 3) (3 x - 2)

Solution steps

\frac{12 x ^{3} + 13 x ^{2} - 59 x + 30}{4 x - 5}

Use the rational root theorem

= \frac{( x + 3 ) \frac{12 x ^{3} + 13 x ^{2} - 59 x + 30}{x + 3}}{4 x - 5}

\frac{12 x ^{3} + 13 x ^{2} - 59 x + 30}{x + 3} = 12 x^{2} - 23 x + 10

= \frac{( x + 3 ) ( 12 x ^{2} - 23 x + 10 )}{4 x - 5}

Factor

12 x^{2} - 23 x + 10 : (3 x - 2) (4 x - 5)

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

Cancel the common factor:

4 x - 5

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

- 3 \times - 2

(3 - x) (- 1 - x)

5 \times \frac{2}{3}

64 b^{3} + 125 a^{3}

lo g_{10} (1100)

What is (12x^3+13x^2-59x+30)/(4x-5) ?
The solution to (12x^3+13x^2-59x+30)/(4x-5) is (x+3)(3x-2)