Precalculus Examples

$f (2) = 2 x^{4} - 8 x^{2} + 5 x - 7$

Step 1

Replace the variable $x$ with $2$ in the expression.

$f (2) = 2 {(2)}^{4} - 8 {(2)}^{2} + 5 (2) - 7$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $2$ by ${(2)}^{4}$ by adding the exponents.

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Step 2.1.1.1

Multiply $2$ by ${(2)}^{4}$ .

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Step 2.1.1.1.1

Raise $2$ to the power of $1$ .

$f (2) = 2 {(2)}^{4} - 8 {(2)}^{2} + 5 (2) - 7$

Step 2.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (2) = 2^{1 + 4} - 8 {(2)}^{2} + 5 (2) - 7$

Step 2.1.1.2

Add $1$ and $4$ .

$f (2) = 2^{5} - 8 {(2)}^{2} + 5 (2) - 7$

Step 2.1.2

Raise $2$ to the power of $5$ .

$f (2) = 32 - 8 {(2)}^{2} + 5 (2) - 7$

Step 2.1.3

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

$f (2) = 32 - 8 \cdot 4 + 5 (2) - 7$

Step 2.1.4

Multiply $- 8$ by $4$ .

$f (2) = 32 - 32 + 5 (2) - 7$

Step 2.1.5

Multiply $5$ by $2$ .

$f (2) = 32 - 32 + 10 - 7$

Step 2.2

Simplify by adding and subtracting.

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Step 2.2.1

Subtract $32$ from $32$ .

$f (2) = 0 + 10 - 7$

Step 2.2.2

Add $0$ and $10$ .

$f (2) = 10 - 7$

Step 2.2.3

Subtract $7$ from $10$ .

$f (2) = 3$

Step 2.3

The final answer is $3$ .

$3$

Step 3