Precalculus Examples

$f (3) = 2 x^{4} - 11 x^{3} + 11 x^{2} + 15 x - 9$

Step 1

Replace the variable $x$ with $3$ in the expression.

$f (3) = 2 {(3)}^{4} - 11 {(3)}^{3} + 11 {(3)}^{2} + 15 (3) - 9$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Raise $3$ to the power of $4$ .

$f (3) = 2 \cdot 81 - 11 {(3)}^{3} + 11 {(3)}^{2} + 15 (3) - 9$

Step 2.1.2

Multiply $2$ by $81$ .

$f (3) = 162 - 11 {(3)}^{3} + 11 {(3)}^{2} + 15 (3) - 9$

Step 2.1.3

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

$f (3) = 162 - 11 \cdot 27 + 11 {(3)}^{2} + 15 (3) - 9$

Step 2.1.4

Multiply $- 11$ by $27$ .

$f (3) = 162 - 297 + 11 {(3)}^{2} + 15 (3) - 9$

Step 2.1.5

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

$f (3) = 162 - 297 + 11 \cdot 9 + 15 (3) - 9$

Step 2.1.6

Multiply $11$ by $9$ .

$f (3) = 162 - 297 + 99 + 15 (3) - 9$

Step 2.1.7

Multiply $15$ by $3$ .

$f (3) = 162 - 297 + 99 + 45 - 9$

Step 2.2

Simplify by adding and subtracting.

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Step 2.2.1

Subtract $297$ from $162$ .

$f (3) = - 135 + 99 + 45 - 9$

Step 2.2.2

Add $- 135$ and $99$ .

$f (3) = - 36 + 45 - 9$

Step 2.2.3

Add $- 36$ and $45$ .

$f (3) = 9 - 9$

Step 2.2.4

Subtract $9$ from $9$ .

$f (3) = 0$

Step 2.3

The final answer is $0$ .

$0$

Step 3