Question

Write the coefficient and index form for the polynomial $3{x^5} - 4x + 9$

Answer 1

Hint: First we have to understand the meaning of the term coefficient, here a coefficient is nothing but a multiplicative factor in a polynomial or in any expression. Generally it is a number but also may be any expression. Coefficients are also called as parameters and are clearly distinguished from other variables. The index form of the polynomial is a number, which says how many times it is used in a multiplication, for example take ${x^2}$ here the index of this expression is 2, which is the exponent or the power.

Complete step by step solution:
Index form is rather called as the exponent or the power of that particular explanation.
The coefficient form of the given polynomial $3{x^5} - 4x + 9$ is:
The coefficient form is $\left( {3,0,0,0, - 4,9} \right)$.
The index form of the given polynomial $3{x^5} - 4x + 9$ is:
The index form is $3{x^5} + 0{x^4} + 0{x^3} + 0{x^2} - 4x + 9$.

The coefficient form is $\left( {3,0,0,0, - 4,9} \right)$ ,
The index form is $3{x^5} + 0{x^4} + 0{x^3} + 0{x^2} - 4x + 9$

Note: Here the coefficient form is the set of coefficients of the given polynomial, which also includes the coefficients of the terms which are not present in the polynomial. Whereas the index form of a polynomial is the whole form of the polynomial such as including the terms with zero coefficients so as to complete the whole form of the polynomial expression.