What is ((4x^8-10x^6-6x^4))/((2x^3)) ?

The solution to ((4x^8-10x^6-6x^4))/((2x^3)) is x(2x^2+1)(x^2-3)

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simplify ((4x^8-10x^6-6x^4))/((2x^3))

simplify

\frac{( 4 x ^{8} - 10 x ^{6} - 6 x ^{4} )}{( 2 x ^{3} )}

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

Solution steps

\frac{4 x ^{8} - 10 x ^{6} - 6 x ^{4}}{2 x ^{3}}

Factor

4 x^{8} - 10 x^{6} - 6 x^{4} : 2 x^{4} (2 x^{4} - 5 x^{2} - 3)

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

Factor

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

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

Cancel the common factor:

2

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

x^{4} = x^{3} x

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

Cancel the common factor:

x^{3}

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

(i) x^{2} + \frac{1}{6} \cdot x - \frac{1}{6}

(4 x + 6 y) (4 x - 6 y)

(3^{x})^{3}

9 a^{2} b^{3} - 16 a^{4} b

\frac{x ^{7}}{( a ^{2} - x ^{2} )}

What is ((4x^8-10x^6-6x^4))/((2x^3)) ?
The solution to ((4x^8-10x^6-6x^4))/((2x^3)) is x(2x^2+1)(x^2-3)