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

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

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

simplify

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

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

Solution steps

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

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

Factor out

x^{3}

from

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

Factor out

- 1

from

- 2 x - 3 : - (2 x + 3)

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

Factor out common term

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

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

Factor

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

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

Cancel the common factor:

2 x + 3

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

\frac{12 f - 32}{( 2 f )}

i^{n} \cdot i^{n + 1} \cdot i^{n + 2} \cdot i^{n + 3}

(a^{2} + b^{2})^{2} - 4 a^{2} \cdot b^{v}

\frac{1}{2 \cdot 1 - ( \frac{n}{2} ) ^{2}}

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

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