Precalculus Examples

$6 x^{2} + 8 x$

Step 1

Factor out the $6$

$6 (x^{2} + \frac{4 x}{3})$

Step 2

To find the $c$ value $c = {(\frac{b}{2})}^{2}$ , divide the coefficient of $x$ by $2$ and square the result.

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Multiply the numerator by the reciprocal of the denominator.

${(\frac{4}{3} \cdot \frac{1}{2})}^{2}$

Cancel the common factor of $2$ .

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Factor $2$ out of $4$ .

${(\frac{2 (2)}{3} \cdot \frac{1}{2})}^{2}$

Cancel the common factor.

${(\frac{2 \cdot 2}{3} \cdot \frac{1}{2})}^{2}$

Rewrite the expression.

${(\frac{2}{3})}^{2}$

Simplify the expression.

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Apply the product rule to $\frac{2}{3}$ .

$\frac{2^{2}}{3^{2}}$

Raise $2$ to the power of $2$ .

$\frac{4}{3^{2}}$

Raise $3$ to the power of $2$ .

$\frac{4}{9}$

Step 3

Add $\frac{4}{9}$ to get the perfect square trinomial.

$6 (x^{2} + \frac{4 x}{3} + \frac{4}{9})$

Step 4

Simplify.

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Apply the distributive property.

$6 x^{2} + 6 \frac{4 x}{3} + 6 (\frac{4}{9})$

Simplify.

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Cancel the common factor of $3$ .

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Factor $3$ out of $6$ .

$6 x^{2} + 3 (2) \frac{4 x}{3} + 6 (\frac{4}{9})$

Cancel the common factor.

$6 x^{2} + 3 \cdot 2 \frac{4 x}{3} + 6 (\frac{4}{9})$

Rewrite the expression.

$6 x^{2} + 2 (4 x) + 6 (\frac{4}{9})$

Multiply $4$ by $2$ .

$6 x^{2} + 8 x + 6 (\frac{4}{9})$

Cancel the common factor of $3$ .

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Factor $3$ out of $6$ .

$6 x^{2} + 8 x + 3 (2) \frac{4}{9}$

Factor $3$ out of $9$ .

$6 x^{2} + 8 x + 3 \cdot 2 \frac{4}{3 \cdot 3}$

Cancel the common factor.

$6 x^{2} + 8 x + 3 \cdot 2 \frac{4}{3 \cdot 3}$

Rewrite the expression.

$6 x^{2} + 8 x + 2 (\frac{4}{3})$

Combine $2$ and $\frac{4}{3}$ .

$6 x^{2} + 8 x + \frac{2 \cdot 4}{3}$

Multiply $2$ by $4$ .

$6 x^{2} + 8 x + \frac{8}{3}$

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