Question

1. evaluate the polynomial $2x^{5}-7x^{4}-5x^{3}+18x^{2}-1$ at $x = -1$.\\$\frac{1}{2}$\\$-13$\\$-\frac{1}{2}$\\$13$

Explanation:

Step1: Substitute \( x = -1 \) into the polynomial \( 2x^5 - 7x^4 - 5x^3 + 18x^2 - 1 \)

For each term:

• Term \( 2x^5 \): \( 2\times(-1)^5 = 2\times(-1) = -2 \)
• Term \( -7x^4 \): \( -7\times(-1)^4 = -7\times1 = -7 \)
• Term \( -5x^3 \): \( -5\times(-1)^3 = -5\times(-1) = 5 \)
• Term \( 18x^2 \): \( 18\times(-1)^2 = 18\times1 = 18 \)
• Constant term \( -1 \): \( -1 \)

Step2: Sum all the terms

\( (-2) + (-7) + 5 + 18 + (-1) \)
First, \( -2 - 7 = -9 \)
Then, \( -9 + 5 = -4 \)
Then, \( -4 + 18 = 14 \)
Then, \( 14 - 1 = 13 \)

Answer:

13