2. thebasicsofpolynomials
➔ Polynomial can be broken down into “poly” and “-nomial”.
◆ poly ➼ “many”
◆ -nomial ➼ “term”
➔ A polynomial is the sum or difference of monomials, binomials, and trinomials.
These polynomials can contain-
◆ constants ➼ a number on it’s own (ex. 3, -20, ½)
◆ variables ➼ a symbol for a number we don’t know yet (x, y)
◆ exponents ➼ a number that says how many times to use the value in multiplication (8² = 8 x 8 = 64)
➔ These polynomials can also be combined by various math operations.
◆ addition / subtraction
◆ multiplication
◆ division / long division
● a polynomial can never be divided by a variable
3. monomials,binomials,andtrinomials
➔ Other kind of expressions used are monomials, binomials, and trinomials. These
kinds of expressions are labeled by the number of terms they each have.
◆ monomial ➼ 1 term
● 3xy²
◆ binomial ➼ 2 terms
● 5x - 1
◆ trinomial ➼ 3 terms
● 3x + 5y² - 3
➔ Polynomials can also have degrees.
◆ the degree of a polynomial with only one variable is the largest exponent of that variable
● 4x³ - x + 3 ➼ the degree of this polynomial is 3.
➔ Most polynomials are written in standard form, which means the terms are
written in descending order.
◆ x⁶ + 4x³ + 3x² - 7
5. addingpolynomials
➔ To add polynomials, add any like terms together.
◆ like terms have the same variables (and their exponents)
equation made using Daum Equation Editor
6. subtractingpolynomials
➔ To subtract polynomials, first reverse the sign of each term that is being
subtracted, and then add as usual.
equation made using Daum Equation Editor
7. multiplyingpolynomials
➔ To multiply 2 polynomials-
◆ multiply each term in one polynomial by each term in the other polynomial
◆ add those answers and simplify if needed
➔ There are many different possibilities when multiplying polynomials-
◆ 1 term x 1 term
● (2xy)(4y) = (2)(4)(xy)(y)
◆ 1 term x 2 terms
● 2x(x+2xy) = (2x + x) + (2x)(3xy) = 2x²+6x²y
◆ 2 terms x 2 terms (FOIL)
● (2x+3)(xz-a)
○ 2x²z-2xa+3xz-3a
◆ 2 terms x 3 terms
● (x+a) (2x+3y-5)
○ 2x²+3xy-5x+2ax+3ay-5a
➔ always remember to add like terms
8. dividingpolynomialspt.1;basicdivision
➔ Some polynomials can be divided using basic division. To do this, it’s easiest to
split the equation at the “+” and “-” signs.
equation made using Daum Equation Editor
- this answer is not a polynomial,
because it contains division by a
variable
9. dividingpolynomialspt.1;usinglongdivision
➔ The top polynomial is the numerator, while the bottom polynomial is the
denominator.
➔ The denominator is written first, while the numerator is written beneath the
radical symbol.
equation made using Daum Equation Editor
10. dividingpolynomials;methodsforlongdivision
01. Divide first term of the numerator by the first term of the denominator
02. Multiply the denominator by that answer, and that below the numerator
03. Subtract to create a new polynomial
equation made using Daum Equation Editor
- if a remainder is left, this
number goes above the bottom
polynomial in the final answer
