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Sagot :
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]
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]
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