Question

Define the value of a polynomial at a point.

Answer 1

Hint: In this question we have to find the value of a polynomial at a point. So we will first try to understand the definition of a polynomial and then we take any value, for better understanding of the polynomial at a point.

Complete step by step solution:
As we know, a polynomial is an algebraic expression that consists of variables, coefficients and exponents.
The general form of an algebraic expression is
 ${a_0}{x^n} + {a_1}{x^{n - 1}} + ... + {a_n}{x^0}$ .
Now the value of the polynomial at a point is defined as the value obtained at a specific point for the given function.
Let us assume the polynomial function be
 $P(x) = x + 1$ .
Now we have to take the value of $x$ to find that value of the polynomial at that point.
So let us take $x = 1$, so we can write the polynomial function as
$P(1) = 1 + 1$
It gives us a value of $2$ .
Therefore we can say that the value of a polynomial means the value that polynomial takes if we substitute the variables with any number.
Hence the value of polynomial $P(x)$ at $x = 1$ is $2$ .

Note: We should note that we can say that if $P(x)$ is a polynomial, then the value of $P(x)$ takes at any $x = a$ is $P(a)$ .
This can be represented as value of
$P(x)$ at $x = a$ is $P(a)$ .
So to find the value of any polynomial at that point, we need to replace $x$ with $a$ . Similarly in the above question, we have replaced the variable $x$ with $1$, So by comparing we can say that we have $a = 1$