Question

Divide. (18x^3 + 12x^2 - 3x) ÷ 6x^2

Answer 1

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:

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

Answer 2

$\bold{[ \ Answer \ ]}$

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

$\bold{[ \ Explanation \ ]}$

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

$\bold{-------------------}$

• $\bold{Rewrite}$

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

• $\bold{Rewrite}$

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

• $\bold{Multiply \ Fractions \ (a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c})}$

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

• $\bold{Rewrite}$

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

• $\bold{Simplify}$

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

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