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Write the general form of a 1st, 2nd, and 3rd degree polynomial [tex]\( P(z) \)[/tex] with coefficients [tex]\( C_0, C_1, \ldots, C_n \)[/tex].

Sagot :

GinnyAnswer
Certainly! Let's go through the general forms of polynomials of different degrees step-by-step.

### 1st Degree Polynomial

For a first-degree polynomial with coefficients [tex]\( C_0 \)[/tex] and [tex]\( C_1 \)[/tex], the general form is:

[tex]\[ P(z) = C_0 + C_1 \cdot z \][/tex]

Here:
- [tex]\( C_0 \)[/tex] is the constant term.
- [tex]\( C_1 \)[/tex] is the coefficient of the linear term [tex]\( z \)[/tex].

### 2nd Degree Polynomial

For a second-degree polynomial with coefficients [tex]\( C_0 \)[/tex], [tex]\( C_1 \)[/tex], and [tex]\( C_2 \)[/tex], the general form is:

[tex]\[ P(z) = C_0 + C_1 \cdot z + C_2 \cdot z^2 \][/tex]

Here:
- [tex]\( C_0 \)[/tex] is the constant term.
- [tex]\( C_1 \)[/tex] is the coefficient of the linear term [tex]\( z \)[/tex].
- [tex]\( C_2 \)[/tex] is the coefficient of the quadratic term [tex]\( z^2 \)[/tex].

### 3rd Degree Polynomial

For a third-degree polynomial with coefficients [tex]\( C_0 \)[/tex], [tex]\( C_1 \)[/tex], [tex]\( C_2 \)[/tex], and [tex]\( C_3 \)[/tex], the general form is:

[tex]\[ P(z) = C_0 + C_1 \cdot z + C_2 \cdot z^2 + C_3 \cdot z^3 \][/tex]

Here:
- [tex]\( C_0 \)[/tex] is the constant term.
- [tex]\( C_1 \)[/tex] is the coefficient of the linear term [tex]\( z \)[/tex].
- [tex]\( C_2 \)[/tex] is the coefficient of the quadratic term [tex]\( z^2 \)[/tex].
- [tex]\( C_3 \)[/tex] is the coefficient of the cubic term [tex]\( z^3 \)[/tex].

These general forms represent the polynomial functions in terms of the variable [tex]\( z \)[/tex] and their respective coefficients.
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