Certainly! Let's evaluate the polynomial [tex]\(-x^3 + 4x - 8\)[/tex] for [tex]\(x = 3\)[/tex].
We start by substituting [tex]\(x = 3\)[/tex] into the polynomial:
[tex]\[
-x^3 + 4x - 8
\][/tex]
First, we calculate [tex]\(3^3\)[/tex]:
[tex]\[
3^3 = 27
\][/tex]
Next, we incorporate the negative sign:
[tex]\[
-27
\][/tex]
Now, we calculate the term [tex]\(4 \cdot 3\)[/tex]:
[tex]\[
4 \times 3 = 12
\][/tex]
Putting it all together:
[tex]\[
-27 + 12 - 8
\][/tex]
We will now perform the addition and subtraction step-by-step:
First, add [tex]\(-27\)[/tex] and [tex]\(12\)[/tex]:
[tex]\[
-27 + 12 = -15
\][/tex]
Then, subtract [tex]\(8\)[/tex]:
[tex]\[
-15 - 8 = -23
\][/tex]
Thus, the value of the polynomial [tex]\(-x^3 + 4x - 8\)[/tex] for [tex]\(x = 3\)[/tex] is:
[tex]\[
\boxed{-23}
\][/tex]
