Question

Consider the expression: $2{x^2} - x + 4$. What is the degree of the expression ? How many terms does the expression have ? Find the value of expression if $x = - 2$ ?

Answer 1

Hint: In the given question, we are given a polynomial expression and we are asked various questions revolving around it. So, we have to answer all the questions by doing some simplification and using some techniques. We are also required to find the value of a function for a certain value of the variable. This question requires us to have the knowledge of basic and simple algebraic rules and operations such as substitution, addition, multiplication, subtraction and many more like these. A thorough understanding of functions and its applications can be of great significance.

Complete step-by-step solution:
In the given question, we are given the expression $\left( {2{x^2} - x + 4} \right)$.
The highest power of the variable in the expression $2{x^2} - x + 4$ is $2$. Hence, the degree of the expression is $2$. So, the given expression is quadratic in x.
Now, we can see clearly that there are three terms in the expression $\left( {2{x^2} - x + 4} \right)$. So, the given expression is trinomial.

Now, we have to find the value of the given function for $x = - 2$.
The value of a function at a certain value of variable is found by substituting the value of variable as specified in the question into the function.
So, we need to replace the variable in the function given to us in the question by the value specified.
So, the function given to us is: $f\left( x \right) = \left( {2{x^2} - x + 4} \right)$.
We are required to find the value of $f\left( { - 2} \right)$ by replacing the value of variable x in the function by $\left( { - 2} \right)$.
Hence, $f\left( x \right) = \left( {2{x^2} - x + 4} \right)$
$ \Rightarrow f\left( { - 2} \right) = 2{\left( { - 2} \right)^2} - \left( { - 2} \right) + 4$
Evaluating the powers of $\left( { - 2} \right)$, we get,
$ \Rightarrow f\left( { - 2} \right) = 2\left( 4 \right) + 2 + 4$
Simplifying the expression, we get,
$ \Rightarrow f\left( { - 2} \right) = 8 + 2 + 4$
Adding up the terms, we get,
$ \Rightarrow f\left( { - 2} \right) = 14$
Hence, we get the value of the required expression $f\left( { - 2} \right)$ as $14$ by replacing the variable in the original function,$f\left( x \right) = 2{x^2} - x + 4$, that is x, by the specified value, that is $\left( { - 2} \right)$.

Note: Such questions that require just simple change of variable can be solved easily by keeping in mind the algebraic rules such as substitution and transposition. Substitution of a variable involves putting a certain value in place of the variable. That specified value may be a certain number or even any other variable.