POLYNOMIALS Naming adding and subtracting NAMING POLYNOMIALS A
POLYNOMIALS Naming, adding, and subtracting
NAMING POLYNOMIALS A polynomial is a monomial or a sum of monomials. Some polynomials have special names. A binomial is the sum of two monomials, and a trinomial is the sum of three monomials. Polynomials with more than three terms have no special names. A monomial is a number, variable or the sum of one of more variables. A binomial is the sum of two monomials, and Trinomial is the sum or three monomials. Monomial Binomial Trinomial 7 3 + 4 y x+y+z 13 n 2 a + 3 c P 2 + 5 p + 4 -5 z 3 6 x 2 + 3 xy 5 x 2 – 3 x – 7 4 ab 3 c 2 7 x – 3 y 3 v 2 – 5 w + 7 z *Any polynomial with more than three terms have no special names. Example: 5 x 3 – 3 x 2 + 6 x – 10 4 -term polynomial
THE DEGREE OF POLYNOMIALS The degree of a polynomial is the greatest exponent of any term in the polynomial. To find the degree of a polynomial, you find the degree of each term. For example the degree of 8 x 5 - 3 x 2 + 2 x – 6 is 5 because it is the greatest exponent included in the polynomial. A polynomial with a degree of zero is a constant, a degree of one is linear, a degree of two is quadratic, and a degree of three is cubic. Polynomial Degree Name -15 0 Constant 3 x – 6 1 Linear 5 x + 7 – 3 x 2 2 Quadratic 15 x 3 + 8 – 2 y 3 Cubic The degree of 4, we will refer to as 4 th degree, the degree of 5, 5 th degree and so forth.
FULL NAME OF A POLYNOMIAL FIRST NAME: NAME USING THE DEGREE LAST NAME: NAME USING # OF TERMS Polynomial Degree Name using degree # of Terms Name using # of terms Full Name 5 x + 1 1 Linear 2 Binomial Linear Binomial -15 0 Constant 1 Monomial Constant Monomial 16 x 2 - 5 x + 3 2 Quadratic 3 Trinomial Quadratic Trinomial 3 x 4 – 7 4 4 th Degree 2 Binomial 4 th Degree Binomial
STANDARD FORM OF A POLYNOMIAL The terms of a polynomial are arranged so that the powers of one variable are in descending (decreasing) order. A. 7 x 2 + 2 x 4 – 11 2 x 4 + 7 x 2 – 11 B. 6 x 2 + 5 – 8 x – 2 x 3 -2 x 3 + 6 x 2 – 8 x + 5
ADDING AND SUBTRACTING POLYNOMIALS Adding polynomials is just a matter of combining like terms, with some order of operations considerations thrown in. As long as you're careful with the minus signs, and don't confuse addition and multiplication, you should do fine. Let’s take a Look at a couple of your examples (-) 1. (4 x 2 +6 x + 7) + (2 x 2 + 1 – 9 x) *Distribute the 5. (2 x 3 + 5 x 2 - 3 x) – (x 3 – 8 x 2 + 11) 2 x 3 + 5 x 2 – 3 x –x 3 + 8 x 2 - 11 6 x 2 - 3 x + 8 x 3 + 13 x 2 - 3 x - 11
- Slides: 6