Precalculus Examples

$\frac{2}{5} x^{\frac{5}{2}} + 2 x^{\frac{3}{2}} + 15 x^{\frac{1}{2}}$

Step 1

Factor $x^{\frac{1}{2}}$ out of $\frac{2}{5} x^{\frac{5}{2}} + 2 x^{\frac{3}{2}} + 15 x^{\frac{1}{2}}$ .

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Step 1.1

Reorder $\frac{2}{5}$ and $x^{\frac{5}{2}}$ .

$x^{\frac{5}{2}} \frac{2}{5} + 2 x^{\frac{3}{2}} + 15 x^{\frac{1}{2}}$

Step 1.2

Factor $x^{\frac{1}{2}}$ out of $x^{\frac{5}{2}} \frac{2}{5}$ .

$x^{\frac{1}{2}} (x^{\frac{4}{2}} \frac{2}{5}) + 2 x^{\frac{3}{2}} + 15 x^{\frac{1}{2}}$

Step 1.3

Factor $x^{\frac{1}{2}}$ out of $2 x^{\frac{3}{2}}$ .

$x^{\frac{1}{2}} (x^{\frac{4}{2}} \frac{2}{5}) + x^{\frac{1}{2}} (2 x^{\frac{2}{2}}) + 15 x^{\frac{1}{2}}$

Step 1.4

Factor $x^{\frac{1}{2}}$ out of $15 x^{\frac{1}{2}}$ .

$x^{\frac{1}{2}} (x^{\frac{4}{2}} \frac{2}{5}) + x^{\frac{1}{2}} (2 x^{\frac{2}{2}}) + x^{\frac{1}{2}} \cdot 15$

Step 1.5

Factor $x^{\frac{1}{2}}$ out of $x^{\frac{1}{2}} (x^{\frac{4}{2}} \frac{2}{5}) + x^{\frac{1}{2}} (2 x^{\frac{2}{2}})$ .

$x^{\frac{1}{2}} (x^{\frac{4}{2}} \frac{2}{5} + 2 x^{\frac{2}{2}}) + x^{\frac{1}{2}} \cdot 15$

Step 1.6

Factor $x^{\frac{1}{2}}$ out of $x^{\frac{1}{2}} (x^{\frac{4}{2}} \frac{2}{5} + 2 x^{\frac{2}{2}}) + x^{\frac{1}{2}} \cdot 15$ .

$x^{\frac{1}{2}} (x^{\frac{4}{2}} \frac{2}{5} + 2 x^{\frac{2}{2}} + 15)$

Step 2

Divide $4$ by $2$ .

$x^{\frac{1}{2}} (x^{2} \frac{2}{5} + 2 x^{\frac{2}{2}} + 15)$

Step 3

Combine $x^{2}$ and $\frac{2}{5}$ .

$x^{\frac{1}{2}} (\frac{x^{2} \cdot 2}{5} + 2 x^{\frac{2}{2}} + 15)$

Step 4

Move $2$ to the left of $x^{2}$ .

$x^{\frac{1}{2}} (\frac{2 \cdot x^{2}}{5} + 2 x^{\frac{2}{2}} + 15)$

Step 5

Multiply $2$ by $x^{2}$ .

$x^{\frac{1}{2}} (\frac{2 x^{2}}{5} + 2 x^{\frac{2}{2}} + 15)$

Step 6

Divide $2$ by $2$ .

$x^{\frac{1}{2}} (\frac{2 x^{2}}{5} + 2 x^{1} + 15)$

Step 7

Simplify.

$x^{\frac{1}{2}} (\frac{2 x^{2}}{5} + 2 x + 15)$

Step 8

Factor.

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Step 8.1

Factor $\frac{1}{5}$ out of each term.

$x^{\frac{1}{2}} (\frac{1}{5} (2 x^{2} + 10 x + 75))$

Step 8.2

Remove unnecessary parentheses.

$x^{\frac{1}{2}} \frac{1}{5} (2 x^{2} + 10 x + 75)$

Step 9

Combine $x^{\frac{1}{2}}$ and $\frac{1}{5}$ .

$\frac{x^{\frac{1}{2}}}{5} (2 x^{2} + 10 x + 75)$