Evaluate Using the Given Value 2x^5-7x^4-5x^3+18x^2-1 at x=-1

$2 x^{5} - 7 x^{4} - 5 x^{3} + 18 x^{2} - 1$ at $x = - 1$

Step 1

Replace the variable $x$ with $- 1$ in the expression.

$2 {(- 1)}^{5} - 7 {(- 1)}^{4} - 5 {(- 1)}^{3} + 18 {(- 1)}^{2} - 1$

Step 2

Simplify each term.

Raise $- 1$ to the power of $5$ .

$2 \cdot - 1 - 7 {(- 1)}^{4} - 5 {(- 1)}^{3} + 18 {(- 1)}^{2} - 1$

Multiply $2$ by $- 1$ .

$- 2 - 7 {(- 1)}^{4} - 5 {(- 1)}^{3} + 18 {(- 1)}^{2} - 1$

Raise $- 1$ to the power of $4$ .

$- 2 - 7 \cdot 1 - 5 {(- 1)}^{3} + 18 {(- 1)}^{2} - 1$

Multiply $- 7$ by $1$ .

$- 2 - 7 - 5 {(- 1)}^{3} + 18 {(- 1)}^{2} - 1$

Raise $- 1$ to the power of $3$ .

$- 2 - 7 - 5 \cdot - 1 + 18 {(- 1)}^{2} - 1$

Multiply $- 5$ by $- 1$ .

$- 2 - 7 + 5 + 18 {(- 1)}^{2} - 1$

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

$- 2 - 7 + 5 + 18 \cdot 1 - 1$

Multiply $18$ by $1$ .

$- 2 - 7 + 5 + 18 - 1$

Step 3

Simplify by adding and subtracting.

Subtract $7$ from $- 2$ .

$- 9 + 5 + 18 - 1$

Add $- 9$ and $5$ .

$- 4 + 18 - 1$

Add $- 4$ and $18$ .

$14 - 1$

Subtract $1$ from $14$ .

$13$