Polynomials

By Will Lampert

What is a polynomial?

Polynomial comes from poly which means many, and nomial which means term, so it essentially means many terms. Polynomials can have constants, variables, and exponents. The only thing a polynomial can never have is division by variables.


These are all examples of polynomials.

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Degrees and Terms

The highest degree on the variable (if there is one) tells us the number of possible solutions. It is also used to describe the polynomial. The number of terms tells us the number of individual parts of a polynomial. The number of terms can also be used to classify polynomials.

1 Term - Monomial - 5

2 Terms - Binomial - 4x + 2

3 Terms - Trinomial - 3x^4 + x + 7

4+ Terms - Polynomial - 4x^5 + x^2 + x 11

Dividing Polynomials

Polynomials can be divided using long division.

1) Write the polynomial as the dividend

2) Write the amount of times the divisor goes into the first term above the second term

3) Multiply the number written in the quotient by the divisor and subtract from the dividend

4) Repeat this process until you get 0 from subtracting or the divisor wont go into the dividend anymore in which you will get a remainder.

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Polynomials can also be divided using synthetic division.

1) Write the polynomial in descending order then remove variables

2) If there is missing parts of the polynomial (Ex. not all degrees of x)

3) Write the solution of the factor to the left of the polynomial. This is the divisor.

4) Bring down the first term and multiply this by the divisor. Take that number and put it below the second term, then add the second term by that number.

5) Take the sum and multiply that by the divisor again. Keep repeating the fourth and fifth step for all terms.

6) If the sum with the last term is not 0 then write the sum as a remainder

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Long Division
Synthetic Division

Summary

Polynomials are expressions of algebraic terms. They have terms and degrees which both define and differentiate them. They can be divided by binomials using both long division and synthetic division.

Upcoming

Quiz on December 7th or 8th

Test on December 10th