Algebra Examples

$f (x) = x^{3} + 2 x^{2} - 5 x + 12$ , $x = - 3$

Step 1

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

$f (- 3) = {(- 3)}^{3} + 2 {(- 3)}^{2} - 5 \cdot - 3 + 12$

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 $3$ .

$f (- 3) = - 27 + 2 {(- 3)}^{2} - 5 \cdot - 3 + 12$

Step 2.1.2

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

$f (- 3) = - 27 + 2 \cdot 9 - 5 \cdot - 3 + 12$

Step 2.1.3

Multiply $2$ by $9$ .

$f (- 3) = - 27 + 18 - 5 \cdot - 3 + 12$

Step 2.1.4

Multiply $- 5$ by $- 3$ .

$f (- 3) = - 27 + 18 + 15 + 12$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $- 27$ and $18$ .

$f (- 3) = - 9 + 15 + 12$

Step 2.2.2

Add $- 9$ and $15$ .

$f (- 3) = 6 + 12$

Step 2.2.3

Add $6$ and $12$ .

$f (- 3) = 18$

Step 2.3

The final answer is $18$ .

$18$

Step 3