Why is it important to learn about polynomial functions?

Polynomials are an important part of the “language” of mathematics and algebra. They are used in nearly every field of mathematics to express numbers as a result of mathematical operations. Polynomials are also “building blocks” in other types of mathematical expressions, such as rational expressions.

Why do we need to find the factor?

Factoring is a common mathematical process used to break down the factors, or numbers, that multiply together to form another number. Some numbers have multiple factors. Factoring is useful in resolving various numbers-related problems.

Why is it useful to express a polynomial function in factored form?

Because a polynomial function written in factored form will have an x-intercept where each factor is equal to zero, we can form a function that will pass through a set of x-intercepts by introducing a corresponding set of factors.

What could represent a polynomial function in the real world?

Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example.

What did you learn about polynomial functions?

One of the most important things to learn about polynomials is how to find their roots. Polynomial functions have special names depending on their degree. A polynomial function of degree zero has only a constant term — no x term.

How do polynomial functions play an important role in the field of mathematics?

Polynomial functions play an important role in mathematics. They are generally simple to compute (requiring only computations that can be done by hand) and can be used to model many real-world phenomena.

What is a polynomial factor?

A factor of polynomial P(x) is any polynomial which divides evenly into P(x). For example, x + 2 is a factor of the polynomial x2 – 4. The factorization of a polynomial is its representation as a product its factors.

What do you know about factors?

factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

What does it mean to say a polynomial is in factored form?

The factored form of a polynomial means it is written as a product of its factors. The factors are also polynomials, usually of lower degree.

Why is it important to factor first the GCF in factoring polynomials?

Factoring is very helpful in simplifying expressions and solving equations involving polynomials. The greatest common factor (GCF) of two numbers is the largest number that divides evenly into both numbers. When factoring a polynomial expression, our first step should be to check for a GCF.

What is the importance of factoring polynomials in our daily life?

The purpose of factoring such functions is to then be able to solve equations of polynomials. For example, the solution to x^2 + 5x + 4 = 0 are the roots of x^2 + 5x + 4, namely, -1 and -4. Being able to find the roots of such polynomials is basic to solving problems in science classes in the following 2 to 3 years.