To find the coefficients of the polynomial function of least degree with a leading coefficient of 1, we need to examine the given polynomial representation:
[tex]\[ f(x) = x^3 + Ax^2 + Bx + C \][/tex]
Where:
- [tex]\(A\)[/tex] is the coefficient of [tex]\(x^2\)[/tex],
- [tex]\(B\)[/tex] is the coefficient of [tex]\(x\)[/tex],
- [tex]\(C\)[/tex] is the constant term.
According to the conditions for the polynomial function of least degree, we determine that:
- [tex]\(A\)[/tex], the coefficient of [tex]\(x^2\)[/tex], is 0.
- [tex]\(B\)[/tex], the coefficient of [tex]\(x\)[/tex], is 0.
- [tex]\(C\)[/tex], the constant term, is 0.
Given these values, the polynomial can be written as follows:
[tex]\[ f(x) = x^3 + 0 \cdot x^2 + 0 \cdot x + 0 \][/tex]
Simplifying this expression, we have:
[tex]\[ f(x) = x^3 \][/tex]
So, the coefficients are:
[tex]\[ A = 0 \][/tex]
[tex]\[ B = 0 \][/tex]
[tex]\[ C = 0 \][/tex]
Therefore, in the blanks provided in the question, we fill in the values as follows:
[tex]\[
\begin{array}{l}
f(x)=x^3 + A x^2 + B x + C \\
A=0 \\
B=0 \\
C=0
\end{array}
\][/tex]
Done.
