Evaluate the Function p(x)=2x^3+4x^2+6x+7 , x=1/2

$p (x) = 2 x^{3} + 4 x^{2} + 6 x + 7$ , $x = \frac{1}{2}$

Replace the variable $x$ with $\frac{1}{2}$ in the expression.

$p (\frac{1}{2}) = 2 {(\frac{1}{2})}^{3} + 4 {(\frac{1}{2})}^{2} + 6 (\frac{1}{2}) + 7$

Simplify the result.

Simplify each term.

Apply the product rule to $\frac{1}{2}$ .

$p (\frac{1}{2}) = 2 (\frac{1^{3}}{2^{3}}) + 4 {(\frac{1}{2})}^{2} + 6 (\frac{1}{2}) + 7$

One to any power is one.

$p (\frac{1}{2}) = 2 (\frac{1}{2^{3}}) + 4 {(\frac{1}{2})}^{2} + 6 (\frac{1}{2}) + 7$

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

$p (\frac{1}{2}) = 2 (\frac{1}{8}) + 4 {(\frac{1}{2})}^{2} + 6 (\frac{1}{2}) + 7$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$p (\frac{1}{2}) = 2 (\frac{1}{2 (4)}) + 4 {(\frac{1}{2})}^{2} + 6 (\frac{1}{2}) + 7$

Cancel the common factor.

$p (\frac{1}{2}) = 2 (\frac{1}{2 \cdot 4}) + 4 {(\frac{1}{2})}^{2} + 6 (\frac{1}{2}) + 7$

Rewrite the expression.

$p (\frac{1}{2}) = \frac{1}{4} + 4 {(\frac{1}{2})}^{2} + 6 (\frac{1}{2}) + 7$

Apply the product rule to $\frac{1}{2}$ .

$p (\frac{1}{2}) = \frac{1}{4} + 4 (\frac{1^{2}}{2^{2}}) + 6 (\frac{1}{2}) + 7$

One to any power is one.

$p (\frac{1}{2}) = \frac{1}{4} + 4 (\frac{1}{2^{2}}) + 6 (\frac{1}{2}) + 7$

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

$p (\frac{1}{2}) = \frac{1}{4} + 4 (\frac{1}{4}) + 6 (\frac{1}{2}) + 7$

Cancel the common factor of $4$ .

Cancel the common factor.

$p (\frac{1}{2}) = \frac{1}{4} + 4 (\frac{1}{4}) + 6 (\frac{1}{2}) + 7$

Rewrite the expression.

$p (\frac{1}{2}) = \frac{1}{4} + 1 + 6 (\frac{1}{2}) + 7$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$p (\frac{1}{2}) = \frac{1}{4} + 1 + 2 (3) (\frac{1}{2}) + 7$

Cancel the common factor.

$p (\frac{1}{2}) = \frac{1}{4} + 1 + 2 \cdot (3 (\frac{1}{2})) + 7$

Rewrite the expression.

$p (\frac{1}{2}) = \frac{1}{4} + 1 + 3 + 7$

Find the common denominator.

Write $1$ as a fraction with denominator $1$ .

$p (\frac{1}{2}) = \frac{1}{4} + \frac{1}{1} + 3 + 7$

Multiply $\frac{1}{1}$ by $\frac{4}{4}$ .

$p (\frac{1}{2}) = \frac{1}{4} + \frac{1}{1} \cdot \frac{4}{4} + 3 + 7$

Multiply $\frac{1}{1}$ by $\frac{4}{4}$ .

$p (\frac{1}{2}) = \frac{1}{4} + \frac{4}{4} + 3 + 7$

Write $3$ as a fraction with denominator $1$ .

$p (\frac{1}{2}) = \frac{1}{4} + \frac{4}{4} + \frac{3}{1} + 7$

Multiply $\frac{3}{1}$ by $\frac{4}{4}$ .

$p (\frac{1}{2}) = \frac{1}{4} + \frac{4}{4} + \frac{3}{1} \cdot \frac{4}{4} + 7$

Multiply $\frac{3}{1}$ by $\frac{4}{4}$ .

$p (\frac{1}{2}) = \frac{1}{4} + \frac{4}{4} + \frac{3 \cdot 4}{4} + 7$

Write $7$ as a fraction with denominator $1$ .

$p (\frac{1}{2}) = \frac{1}{4} + \frac{4}{4} + \frac{3 \cdot 4}{4} + \frac{7}{1}$

Multiply $\frac{7}{1}$ by $\frac{4}{4}$ .

$p (\frac{1}{2}) = \frac{1}{4} + \frac{4}{4} + \frac{3 \cdot 4}{4} + \frac{7}{1} \cdot \frac{4}{4}$

Multiply $\frac{7}{1}$ by $\frac{4}{4}$ .

$p (\frac{1}{2}) = \frac{1}{4} + \frac{4}{4} + \frac{3 \cdot 4}{4} + \frac{7 \cdot 4}{4}$

Combine the numerators over the common denominator.

$p (\frac{1}{2}) = \frac{1 + 4 + 3 \cdot 4 + 7 \cdot 4}{4}$

Simplify each term.

Multiply $3$ by $4$ .

$p (\frac{1}{2}) = \frac{1 + 4 + 12 + 7 \cdot 4}{4}$

Multiply $7$ by $4$ .

$p (\frac{1}{2}) = \frac{1 + 4 + 12 + 28}{4}$

Simplify by adding numbers.

Add $1$ and $4$ .

$p (\frac{1}{2}) = \frac{5 + 12 + 28}{4}$

Add $5$ and $12$ .

$p (\frac{1}{2}) = \frac{17 + 28}{4}$

Add $17$ and $28$ .

$p (\frac{1}{2}) = \frac{45}{4}$

The final answer is $\frac{45}{4}$ .

$\frac{45}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{45}{4}$

Decimal Form:

$11.25$

Mixed Number Form:

$11 \frac{1}{4}$

Evaluate the Function p(x)=2x^3+4x^2+6x+7 , x=1/2

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