Question

Write your answer in order of decreasing powers of x.

(18x 5 + 6x 4 - 12x 3) ÷ 6x 2

Answer 1

$\frac{18x^5 +6x^4 - 12x^3}{6x^2} = \frac{(6x^2)(3x^3 +x^2 - 2x)}{6x^2} = 3x^3 +x^2 - 2x$

Answer 2

The answer is:  " 3x³ + x² − 2x " .
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Explanation:
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Take the first expression; or the "numerator" ; 

and  "factor out"  a:  " 6x² " :
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 $\frac{18x^5+6x^4-12x^3}{6 x^{2} } = \frac{6x^2(3x^3+x^2-2x)}{6x^2}$  ;

→  Both  " 6x² " values "cancel out to 1" ;  

     →  since:  " { 6x² / 6x² = 1 } " ; 

And we have:   " 3x³ + x² − 2x " . 
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