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

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

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simplify ((2x^4+4x^3-5x^2+2x-3))/((2x^2+1))

simplify

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

(x - 1) (x + 3)

Solution steps

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

Use the rational root theorem

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

\frac{2 x ^{4} + 4 x ^{3} - 5 x ^{2} + 2 x - 3}{x - 1} = 2 x^{3} + 6 x^{2} + x + 3

= \frac{( x - 1 ) ( 2 x ^{3} + 6 x ^{2} + x + 3 )}{2 x ^{2} + 1}

Factor

2 x^{3} + 6 x^{2} + x + 3 : (x + 3) (2 x^{2} + 1)

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

Cancel the common factor:

2 x^{2} + 1

= (x - 1) (x + 3)

\frac{3 a + 2}{2} - \frac{2 a + 1}{2}

\frac{12}{24}

\frac{12}{15}

\frac{18 x ^{5} y ^{4}}{- 6 x y ^{2}}

2 x^{2} - 6 x y + 4 y^{2}

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