Question

How do you interpret algebraic expression in terms of their context?

Answer 1

Hint: An algebraic expression is made up of variables, coefficients, constant, and terms. A variable is the symbol we use in an expression. The coefficient is the number that follows a variable. A constant is a number without a variable. The result of an expression depends upon the arithmetic we are referring to in mathematics.

Complete step by step solution:
Algebraic expressions in mathematics are made up of variables, constants, and operators.
Every algebraic expression has variables, coefficients, constants, and terms.
Arithmetic operations like addition, subtraction, multiplication, and division can be performed on Algebraic expressions.
An Algebraic expression can be identified by a number of terms
1. A monomial has only one term
2. A binomial has two terms
3. A trinomial has three terms
An Algebraic expression can be identified based on the highest exponent term in an expression
1. If the highest exponent is 0, then it is said to be a constant
2. If the highest exponent is 1, then it is said to be a linear expression
3. If the highest exponent is 2, then it is said to be a quadratic expression
4. If the highest exponent is 3, then it is said to be a cubic expression
The result of an expression depends upon the arithmetic we are referring to in mathematics.
Let us understand the result of the expression through examples,
Example1:
In integer arithmetic,
the result of $5\div 2=\dfrac{5}{2}$that results in 2 with remainder one.
In rational arithmetic,
The result of $5\div 2$ is given by $\dfrac{5}{2}$
Example2:
In real arithmetic,
The quadratic expression ${{x}^{2}}+x+1=0$ has no roots.
In complex arithmetic,
The quadratic expression
${{x}^{2}}+x+1=0$
 has two roots that are given by
$\Rightarrow x=\dfrac{\left( -1+i\sqrt{3} \right)}{2}$ and
 $\Rightarrow x=\dfrac{\left( -1-i\sqrt{3} \right)}{2}$

Note: Every Algebraic expression has numbers, variables, and operations. The expressions can be identified by a number of terms and are also classified based on the highest exponent of any one of the terms in the expression.