Question

What is the general form of first degree polynomial in one variable?

Answer 1

Hint: This problem comes under algebra which we have asked to write the general form of first degree polynomial in one variable. First we need to know about first degree polynomials which are also known as linear polynomials. The equation of the straight line in one axis. Then we need to know about a variable, it is a term or symbol for a number we don’t know yet. It is usually a letter from an alphabet example: a, b, x, y. In other words, algebraic expression letters represent variables. Here asked to find the general form in one variable.

Complete step-by-step solution:
Here we take the one variable as $x$
The general form to find the nth degree of polynomial is
\[{{\text{a}}_{\text{0}}}{{\text{x}}^{\text{n}}}{\text{ + }}{{\text{a}}_{\text{1}}}{{\text{x}}^{{\text{n - 1}}}}{\text{ + }}................{\text{ + }}{{\text{a}}_{{\text{n - 1}}}}{{\text{x}}^{\text{1}}}{\text{ + }}{{\text{a}}_{{\text{n,}}}}\]
\[{{\text{a}}_{\text{0}}}{\text{,}}{{\text{a}}_{\text{1}}}{\text{,}}{{\text{a}}_{{\text{n - 1,}}}}{{\text{a}}_{\text{n}}}{\text{ are real coefficients and where }}{{\text{a}}_{\text{0}}} \ne {\text{0}}\]
By using general form of nth degree of polynomial we find the general form of first degree polynomial in one variable is
Here n=1.
So, ${a_0}{x^1} + {a_1}$\[{\text{where }}{{\text{a}}_{\text{0}}} \ne {\text{0}}\]
Here we represent real coefficients as a and b,
$ax + b = 0$

The general form of first degree polynomial in one variable is $ax + b = 0$

Note: This kind problem needs attention in the general form of nth degree of polynomial. By using this we can find any nth degree of polynomial. Similarly we found the first degree of polynomial which we are familiar with. The basic thing we need to understand is the type of question they asked and we must be familiar with all of the general form in algebra which may be useful to find the solutions.