What is (8x^6-10x^4-12x^3)/(-4x^2) ?

The solution to (8x^6-10x^4-12x^3)/(-4x^2) is -(x(2x-3)(2x^2+3x+2))/2

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simplify (8x^6-10x^4-12x^3)/(-4x^2)

simplify

\frac{8 x ^{6} - 10 x ^{4} - 12 x ^{3}}{- 4 x ^{2}}

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

Solution steps

\frac{8 x ^{6} - 10 x ^{4} - 12 x ^{3}}{- 4 x ^{2}}

Factor

8 x^{6} - 10 x^{4} - 12 x^{3} : 2 x^{3} (4 x^{3} - 5 x - 6)

= \frac{2 x ^{3} ( 4 x ^{3} - 5 x - 6 )}{- 4 x ^{2}}

Factor

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

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

Factor the number:

4 = 2 \cdot 2

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

Cancel the common factor:

2

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

Apply exponent rule:

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

x^{3} = x^{2} x

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

Cancel the common factor:

x^{2}

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

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

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

- x^{2} - 4

\frac{225}{180}

\frac{1}{2} sin (2 x)

(7 - i) (1 + 5 i)

ab - b^{2}

What is (8x^6-10x^4-12x^3)/(-4x^2) ?
The solution to (8x^6-10x^4-12x^3)/(-4x^2) is -(x(2x-3)(2x^2+3x+2))/2