Introducing Polynomials
In this chapter you will use polynomials, a part of algebra, to help explain how games, puzzle, and number tricks.
Polynomials: are algebraic expressions that are formed by combining numbers, variables, and exponents into algebraic terms.
Example: 3x², 5t²
Terms: Are separated by addition and subtraction signs. The expressions -4x2 is just one term because there are no addition or subtraction signs present.
-As you should already know a number that stands alone without any variables connected to it is called a constant. Example: 8 and 2/3 *note there is no variable connected to either!
-A number that multiplies the variable is called a coefficient. Example: 3n-2, the coefficient is 3. In 8x+4, the coefficient is 8
-A polynomial with 1 term is called a monomial. Example: 8y, 2/7, and 9yz
-A polynomial with 2 terms is called a binomial. Example: 2x+3 and 4c³-7c
-A polynomial with 3 terms is called a trinomial. Example: x²+3x-5 and 2xy+5x+9
-An expression with 4 or more terms is called a polynomial Example 4x²+3x-7xy+2
Example: 3x², 5t²
Terms: Are separated by addition and subtraction signs. The expressions -4x2 is just one term because there are no addition or subtraction signs present.
-As you should already know a number that stands alone without any variables connected to it is called a constant. Example: 8 and 2/3 *note there is no variable connected to either!
-A number that multiplies the variable is called a coefficient. Example: 3n-2, the coefficient is 3. In 8x+4, the coefficient is 8
-A polynomial with 1 term is called a monomial. Example: 8y, 2/7, and 9yz
-A polynomial with 2 terms is called a binomial. Example: 2x+3 and 4c³-7c
-A polynomial with 3 terms is called a trinomial. Example: x²+3x-5 and 2xy+5x+9
-An expression with 4 or more terms is called a polynomial Example 4x²+3x-7xy+2
The degree of a polynomial: is not found by adding the degrees of each of each of the terms. Instead, the degree of a polynomial is equal to the degree of the highest exponent.
The degree of The Term: Is found by adding all of the exponents together. The variables, if without an exponent, also count as one exponents too. Example: 7ab The degree of the term is 2 because a and b count for 1 each.
The degree of The Term: Is found by adding all of the exponents together. The variables, if without an exponent, also count as one exponents too. Example: 7ab The degree of the term is 2 because a and b count for 1 each.
![Picture](/uploads/2/8/6/5/28654915/3047895.png)
Adding Polynomials
When you add and subtract polynomials you must combined like terms. If there are variables that are alone, then they are the same (3x would be like terms with 4y). If the variables have exponent numbers that are the same then they are lie terms, (3x¹ and 4y³ would not be like terms.
When you add and subtract polynomials you must combined like terms. If there are variables that are alone, then they are the same (3x would be like terms with 4y). If the variables have exponent numbers that are the same then they are lie terms, (3x¹ and 4y³ would not be like terms.
![Picture](/uploads/2/8/6/5/28654915/3053147.png)
Subtracting Polynomials
In this case you would keep-switch-flip. Keep the first set of polynomials, the change the subtraction sign to an addition sign, and then change every symbol that is in front of the second set of polynomials to the opposite sign.
In this case you would keep-switch-flip. Keep the first set of polynomials, the change the subtraction sign to an addition sign, and then change every symbol that is in front of the second set of polynomials to the opposite sign.
Try this!
![Picture](/uploads/2/8/6/5/28654915/637891.png?97)
Is this a monomial, or a trinomial?
![Picture](/uploads/2/8/6/5/28654915/9905384.png)
Is this a polynomial or a binomial?