Precalculus Examples

$P (x) = x^{3} + 2 x^{2} - 4 x - 1$ , $P C (\frac{1}{2})$

Step 1

Apply the distributive property.

$(x^{3} C + 2 x^{2} C - 4 x C - 1 C) \frac{1}{2}$

Step 2

Rewrite $- 1 C$ as $- C$ .

$(x^{3} C + 2 x^{2} C - 4 x C - C) \frac{1}{2}$

Step 3

Apply the distributive property.

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

Step 4

Simplify.

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Step 4.1

Multiply $x^{3} C \frac{1}{2}$ .

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Step 4.1.1

Combine $x^{3}$ and $\frac{1}{2}$ .

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

Step 4.1.2

Combine $C$ and $\frac{x^{3}}{2}$ .

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

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Factor $2$ out of $2 x^{2} C$ .

$\frac{C x^{3}}{2} + 2 (x^{2} C) \frac{1}{2} - 4 x C \frac{1}{2} - C \frac{1}{2}$

Step 4.2.2

Cancel the common factor.

$\frac{C x^{3}}{2} + 2 (x^{2} C) \frac{1}{2} - 4 x C \frac{1}{2} - C \frac{1}{2}$

Step 4.2.3

Rewrite the expression.

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

Step 4.3

Cancel the common factor of $2$ .

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Step 4.3.1

Factor $2$ out of $- 4 x C$ .

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

Step 4.3.2

Cancel the common factor.

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

Step 4.3.3

Rewrite the expression.

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

Step 4.4

Combine $\frac{1}{2}$ and $C$ .

$\frac{C x^{3}}{2} + x^{2} C - 2 x C - \frac{C}{2}$

Step 5

Reorder $x^{2}$ and $C$ .

$\frac{C x^{3}}{2} + C x^{2} - 2 x C - \frac{C}{2}$

Step 6

Move $x$ .

$\frac{C x^{3}}{2} + C x^{2} - 2 C x - \frac{C}{2}$