Naming Polynomials

Polynomials are the equations of expressions formed by algebraic terms. The algebraic expressions are those that have variables such as x, y, z, whose values keep changing. By combining these variables and constants, we get polynomials.

In mathematics, there are various ways to name polynomials. One way is based on the number of terms, and the other way is based on the degree of the polynomial. In this article, we will learn about both the methods of naming polynomials along with examples.

Naming polynomials

Based on the degree of the polynomials, they can be differentiated as:

• Linear polynomial

• Quadratic polynomial

• Cubic polynomial

Linear polynomials

A linear polynomial is the type of polynomial that has a degree that equals 1. A linear equation always consists of a variable of a single power.

There are various types of linear equations, such as linear equations in one variable, two variables, etc.

As the number of variables increases, the name of equations changes respectively, the equation with a single variable is known as a linear equation in one variable. The equation with two variable types is known as a linear equation in two variables.

The standard form of linear equation is ax+b=c, where a, b and c are real numbers.

For example:

5x+6=1 (with one variable)

42x+32y=60 (with two variables)

Quadratic polynomials

An equation in which the variable’s highest degree is 2 is said to be a quadratic polynomial. The standard form of this polynomial in any variable (x) is ax2+ bx + c = 0, where a, b, and c are real numbers. Here, x is variable and a ≠ 0. The quadratic polynomial is a second-order polynomial equation with a single variable. Its solution may be real or complex.

For example, 6x² + 10x + 6 =0 is a quadratic polynomial.

The standard form of a quadratic polynomial is ax2+bx+c=0.

(b2- 4ac), is called the discriminant of the equation and is represented by ‘D’.

D> 0, the quadratic equation will have unequal and real roots.

D = 0, the quadratic equation will have two equal and real roots.

D < 0, the quadratic equation will have complex roots.

Cubic equation

A polynomial in which the constraint’s highest degree is 3 is said to be a cubic polynomial. In this equation, the highest exponent remains to be always 3. Standard form of the cubic equation in any variable (x) is ax³ + bx² + cx + d = 0

For example:

x³+ 3=0

2x³+4x=0

4x³+ x²+ 4x-8=0

Naming polynomials based on the number of terms

Before learning about the multiplying of polynomials, let us understand the types of polynomials on the basis of the number of terms:

• Monomial: Polynomials that have only one term are known as monomials. For example, 3x, 7xy, 5, 4x².

• Binomial: Polynomials that have two terms are known as binomial. For example, 3x + 4, 4x²+3, 5z + 3x.

• Trinomial: Polynomials that have three terms are known as trinomials. For example, 3x + 5y + 6, x²+3x+3, 5z + 3x + 3.

Types of inequalities in mathematics

• Strict inequality: This inequality has > or < symbol between the left-hand side and the right-hand side.

• Slack inequality: This inequality has ≤ or ≥ between the left-hand side and the right-hand side.

• Linear inequality:  This inequality has a degree 1. For example, 5x + 2y > 10

• Quadratic inequality: This inequality has a degree 2. For example, 10x² + 8y > 44

Conclusion

Polynomial is an expression formed by the combination of variables and constants. We can name the polynomials based on the number of terms and degrees of polynomials. As per the degree, the polynomials are named linear polynomials, quadratic polynomial and cubic polynomials.

Further, based on the number of terms, the polynomials are monomial, binomial and trinomial. We can perform all the arithmetic operations such as addition, subtraction, multiplication and division on the polynomials.