Question

What is the coefficient of ${{x}^{3}}$ in $2-{{x}^{3}}+{{x}^{2}}$ ?

Answer 1

Hint: Here we have to find the coefficient of a term in the algebraic expression given. Firstly as we know that the coefficient is a constant value along with the sign of the particular unknown variable. So firstly we will find how many terms whose coefficient is to be determined are in the algebraic expression. Then we will write down the coefficient from it and get our desired answer.

Complete step-by-step answer:
The algebraic expression is given as follows:
$2-{{x}^{3}}+{{x}^{2}}$ ……$\left( 1 \right)$
We have to find the coefficient of ${{x}^{3}}$ term in the above algebraic expression. It is clear that it is a polynomial expression as it has more than one term with non-negative integral exponent in it.
As we can see that there is only one term of that variable whose power is $3$ so we don’t have to simplify the expression further.
On comparing equation (1) by ${{x}^{3}}$ we get,
$2-{{x}^{3}}+{{x}^{2}}={{x}^{3}}$
So the coefficient of ${{x}^{3}}$ is $-1$
Hence the coefficient of ${{x}^{3}}$ in $2-{{x}^{3}}+{{x}^{2}}$ is $-1$ .
So, the correct answer is “-1”.

Note: An algebraic expression is a mathematical expression made up of unknown variables, constant, coefficient and algebraic operation such as addition, subtraction, multiplication and division. An algebraic expression is without an equal sign that is it has no sides. There are three types of algebraic expressions such as monomial expression, binomial expression and polynomial expression. The only difference in all of them is the number of terms. We know that each term in an algebraic expression is separated by $+$ or $-$ sign and each variable is multiplied by a constant term that constant term multiplied to any variable is known as its coefficient.