Sure, let's evaluate the polynomial [tex]\(5x - 4x^2 + 3\)[/tex] at the given values of [tex]\(x\)[/tex].
### Step-by-Step Solution:
1. Evaluating the polynomial at [tex]\(x = 0\)[/tex]:
[tex]\[ 5(0) - 4(0)^2 + 3 \][/tex]
[tex]\[ = 0 - 0 + 3 \][/tex]
[tex]\[ = 3 \][/tex]
So, the value of the polynomial at [tex]\(x = 0\)[/tex] is [tex]\(\boxed{3}\)[/tex].
2. Evaluating the polynomial at [tex]\(x = -1\)[/tex]:
[tex]\[ 5(-1) - 4(-1)^2 + 3 \][/tex]
[tex]\[ = -5 - 4(1) + 3 \][/tex]
[tex]\[ = -5 - 4 + 3 \][/tex]
[tex]\[ = -6 \][/tex]
So, the value of the polynomial at [tex]\(x = -1\)[/tex] is [tex]\(\boxed{-6}\)[/tex].
3. Evaluating the polynomial at [tex]\(x = 2\)[/tex]:
[tex]\[ 5(2) - 4(2)^2 + 3 \][/tex]
[tex]\[ = 10 - 4(4) + 3 \][/tex]
[tex]\[ = 10 - 16 + 3 \][/tex]
[tex]\[ = -3 \][/tex]
So, the value of the polynomial at [tex]\(x = 2\)[/tex] is [tex]\(\boxed{-3}\)[/tex].
Thus, the values of the polynomial [tex]\(5x - 4x^2 + 3\)[/tex] at [tex]\(x = 0\)[/tex], [tex]\(x = -1\)[/tex], and [tex]\(x = 2\)[/tex] are 3, -6, and -3, respectively.
