12.2 Polynomial components

Previously, we discussed Polynomials and Multiplication and division of polynomials. From there we learned that Polynomials are expressions that contain terms which are comprised of the combination of a coefficient, a constant, variables and exponents. We also learned that it can come in different forms depending on the number of terms that the expression has, monomial for one term, binomial for two terms, trinomial for three terms and polynomial for more than three terms.

These terms can be combined through the four different operations namely addition, subtraction, multiplication and division with the exemption of division wherein the denominator is a variable. In this chapter we will focus a bit more in multiplying polynomials, particularly monomial by monomials, monomials by binomials, binomial by binomial and polynomial by polynomial.

Apart from the terms there are also other components of a polynomial. In previous chapter, we learned that each term of the polynomial has a degree, and it is denoted by its exponent. We also learned that the highest degree of the polynomial indicates the degree of the polynomial. So if you’re given the term 5x, you will know that it’s degree is 1. If you’re given the expression 5x3+2x25x^3 + 2x^2, the degree of each terms are, 3, and 2 respectively, and the degree of the polynomial is 3.

We will also look into the application of polynomials in solving for problems in geometry especially that of finding the area of shaded regions and non shaded regions. To illustrate this application you can try graphing polynomial expressions with a free polynomial graphing tool online.

Polynomial components

Polynomials can involve a long string of terms that are difficult to comprehend. So, before we dive into more complex polynomial concepts and calculations, we need to understand the components of polynomials and be able to identify its terms, coefficients, degree, leading term, and leading coefficient.

Lessons

  • 1.
    Describe the following polynomial:
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Polynomial components

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