Solve (x^6+2x^3-1/2x^2)div(-1/2x)^2

$$( x ^ { 6 } + 2 x ^ { 3 } - \frac { 1 } { 2 } x ^ { 2 } ) \div ( - \frac { 1 } { 2 } x ) ^ { 2 }$$

Evaluate

$$4x^{4}+8x-2$$

Short Solution Steps

Expand \left(-\frac{1}{2}x\right)^{2}.

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

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{x^{6}+2x^{3}-\frac{1}{2}x^{2}}{\frac{1}{4}x^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out x^{2} in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{4}+2x-\frac{1}{2}}{\frac{1}{4}}$$

Divide x^{4}+2x-\frac{1}{2} by \frac{1}{4} by multiplying x^{4}+2x-\frac{1}{2} by the reciprocal of \frac{1}{4}.

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

Use the distributive property to multiply x^{4}+2x-\frac{1}{2} by 4.

$$4x^{4}+8x-2$$

Expand

$$4x^{4}+8x-2$$

Short Solution Steps

Expand \left(-\frac{1}{2}x\right)^{2}.

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

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{x^{6}+2x^{3}-\frac{1}{2}x^{2}}{\frac{1}{4}x^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out x^{2} in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{4}+2x-\frac{1}{2}}{\frac{1}{4}}$$

Divide x^{4}+2x-\frac{1}{2} by \frac{1}{4} by multiplying x^{4}+2x-\frac{1}{2} by the reciprocal of \frac{1}{4}.

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

Use the distributive property to multiply x^{4}+2x-\frac{1}{2} by 4.

$$4x^{4}+8x-2$$