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Individuals spend too much time in algebra solving polynomial equations or factoring polynomials. A polynomial function involves only non-negative integer powers of x, such as a cubic, quadratic, or quartic function. In many college algebra solutions, polynomial functions are used to describe common functions. To master the techniques, one must perform numerous practice exercises until they become natural and easy. Below is a guide on how to make studying polynomial functions easy.

What are Polynomial Functions?

Polynomial is composed of the words 'poly' and 'nomial.' Because poly means ‘many’ and ‘nomial’ means ‘term,’ ‘polynomials’ can be simply termed as algebraic expressions with several terms when they are combined. Polynomial functions are expressions that can have variable degrees, positive exponents, coefficients, and constants.

Understand the Types of Polynomial Functions

The number of terms in a polynomial determines its name. The three common polynomials students encounter are:

Polynomials with only one term known as Monomials. 15x2, 12y4, and 3b are some examples.

Polynomials with only two terms are known as Binomials. 4x – 7, x + y, and 9x + 2 are some examples.

Polynomial with only three terms known as 'trimonials.' z4 + 45 + 3z,  x3 – 3 + 5x, and x2 – 12x + 15 are some examples.

Furthermore, polynomials are classified according to their degrees. Zero polynomial function, quadratic polynomial function, linear polynomial function, and cubic polynomial function are the top four types of polynomials used in algebra and precalculus.

Graphing Polynomial Function

All polynomial functions can be represented graphically by students. When solving graphs of polynomial functions, one should remember that any polynomial function's domain is the set of all real numbers. Recognizing the connection between equations and their graphs is essential in coordinate geometry. A straight line is represented by a linear polynomial function of the form y = ax + b, a parabola is represented by a quadratic polynomial function of the form y = ax2 + bx + c and a cubic polynomial function takes the form of y = ax3 + bx2 + cx + d.

How to Determine a Polynomial Function

For one to determine whether a function is polynomial or not, the exponents of the variables must be evaluated against certain conditions. Some learners find it hard to comprehend these concepts; those that want more practice and need algebra 2 problems and answers can visit the PlainMath platform for assistance. The following are the conditions for determining polynomial functions:

Every term's exponent of the variable in the function must be a non-negative whole figure. In other words, the variable's exponent should not be a negative number or a fraction.

The function's variable should not be contained within a radical; it should not consist of any square roots or cube roots.

The variable must not be included in the denominator.

Conclusion

Polynomials are an essential math and algebraic language. They are used to express figures as a result of mathematical operations in virtually all areas of mathematics. Polynomials can also be used to construct other forms of mathematical expressions, like rational expressions.