Question

Write the general form of the linear polynomial and cubic polynomial.

Answer 1

Hint: A polynomial is an expression that can be built from constants and symbols called variables or indeterminants by means of addition, multiplication and exponentiation to a non-negative integer power. degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. For a univariate polynomial, the degree of the polynomial is simply the highest exponent occurring in the polynomial.

Complete step-by-step answer:
A polynomial in a single indeterminate x can always be written (or rewritten) in the form
\[{a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + .......{a_2}{x^2} + {a_1}x + {a_0}\] where \[{a_0},{a_1}......,{a_n}\] are constants and \[x\] is the indeterminate. The word “indeterminate” means that \[x\] represents no particular value , although any value may be substituted for it.
The following names are assigned to polynomials according to their degree:
Degree \[0\] – non-zero constant
Degree \[1\] – linear
Degree \[2\] – quadratic
Degree \[3\] – cubic
Degree \[4\] – quartic (or, if all terms have even degree, biquadratic)
Degree \[5\] – quintic
Degree \[6\] – sextic (or, less commonly, hexic)
Degree \[7\] – septic (or, less commonly, heptic)
For higher degrees, names have sometimes been proposed] but they are rarely used:
Degree \[8\] – octic
Degree \[9\] – nonic
Degree \[10\] – decic
General form of a linear polynomial is \[ax + b\] where \[a\] and \[b\] are constants and \[x\] is a variable.
General form of a cubic polynomial is \[a{x^3} + b{x^2} + cx + d\] where \[a,b,c,d\] are constants and \[x\] is a variable.

Note: Take care that the polynomial is in one variable or more than one variables.if it is in one variable, the degree is simply the highest exponent occurring in the polynomial. If it is in more than one variable, the degree is the highest sum of exponents occurring in the polynomial.