Question

evaluate the function for the given value of x.
p(x) = -x^5 + 11x^3 + 7 ; x = 3
p(3) = \square

Explanation:

Step1: Substitute \( x = 3 \) into \( p(x) \)

Substitute \( x = 3 \) into the function \( p(x)=-x^{5}+11x^{3}+7 \), we get \( p(3)=-(3)^{5}+11\times(3)^{3}+7 \).

Step2: Calculate each term

First, calculate \( (3)^{5}=243 \), so \( -(3)^{5}=-243 \). Then, calculate \( (3)^{3}=27 \), so \( 11\times(3)^{3}=11\times27 = 297 \).

Step3: Sum up the terms

Now, sum up the three terms: \( p(3)=-243 + 297+7 \). Calculate \( -243+297 = 54 \), then \( 54 + 7=61 \).

Answer:

\( 61 \)