Question

Divide. (18x^3 + 12x^2 - 3x) ÷ 6x^2

Answer 1

`\bold{[ \ Answer \ ]}`

`\boxed{\bold{(x^3\left(6x^2+4x-1\right))/(2)}}`

`\bold{[ \ Explanation \ ]}`

• 
  `\bold{Divide: \ \left(18x^3\:+\:12x^2\:-\:3x\right)\:/ \:6x^2}`

`\bold{-------------------}`

• 
  `\bold{Rewrite}`

`\bold{18x^3+12x^2-3x \ = \ x^2(x\left(6x^2+4x-1\right))/(2)}`

• 
  `\bold{Rewrite}`

`\bold{x^2(x\left(6x^2+4x-1\right))/(2)}`

• 
  `\bold{Multiply \ Fractions \ (a\cdot (b)/(c)=(a\:\cdot \:b)/(c))}`

`\bold{(x\left(6x^2+4x-1\right)x^2)/(2)}`

• 
  `\bold{Rewrite}`

`\bold{x\left(6x^2+4x-1\right)x^2 \ = \ x^3\left(6x^2+4x-1\right)}`

• 
  `\bold{Simplify}`

`\bold{(x^3\left(6x^2+4x-1\right))/(2)}`

`\boxed{\bold{[] \ Eclipsed \ []}}`

Answer 2

For this case, we must divide the following expression:

`\frac {18x ^ 3 + 12x ^ 2-3x} {6x ^ 2} =`

We separate:

`\frac {18x ^ 3} {6x ^ 2} + \frac {12x ^ 2} {6x ^ 2} - \frac {3x} {6x ^ 2} =`

By definition of power properties we have to:

`\frac {a ^ m} {a ^ n} = a ^ {m-n}`

So:

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

By definition of power properties we have to:

`a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}`

Then:

`3x + 2- \frac {1} {2} * \frac {1} {x} =\\3x + 2- \frac {1} {2x}`

Answer:

`3x + 2- \frac {1} {2x}`