What is ((2x^4+5x^3+3x^2+8x+12))/((2x+3)) ?

The solution to ((2x^4+5x^3+3x^2+8x+12))/((2x+3)) is (x+2)(x^2-x+2)

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simplify ((2x^4+5x^3+3x^2+8x+12))/((2x+3))

simplify

\frac{( 2 x ^{4} + 5 x ^{3} + 3 x ^{2} + 8 x + 12 )}{( 2 x + 3 )}

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

Solution steps

\frac{2 x ^{4} + 5 x ^{3} + 3 x ^{2} + 8 x + 12}{2 x + 3}

Use the rational root theorem

= \frac{( x + 2 ) \frac{2 x ^{4} + 5 x ^{3} + 3 x ^{2} + 8 x + 12}{x + 2}}{2 x + 3}

\frac{2 x ^{4} + 5 x ^{3} + 3 x ^{2} + 8 x + 12}{x + 2} = 2 x^{3} + x^{2} + x + 6

= \frac{( x + 2 ) ( 2 x ^{3} + x ^{2} + x + 6 )}{2 x + 3}

Factor

2 x^{3} + x^{2} + x + 6 : (2 x + 3) (x^{2} - x + 2)

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

Cancel the common factor:

2 x + 3

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

e^{x^{- 1}}

10 x - 20

10 x - 15

\frac{85 - 100}{15}

lo g_{13} (\frac{1}{13})

What is ((2x^4+5x^3+3x^2+8x+12))/((2x+3)) ?
The solution to ((2x^4+5x^3+3x^2+8x+12))/((2x+3)) is (x+2)(x^2-x+2)