POLYNOMIALS Naming, adding, and subtracting. NAMING POLYNOMIALS A polynomial is a monomial or a sum of monomials. Some polynomials have special names.

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Presentation transcript:

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. *Any polynomial with more than three terms have no special names. Example: 5x 3 – 3x 2 + 6x – 10 4-term polynomial MonomialBinomialTrinomial yx + y + z 13n2a + 3cP 2 + 5p z 3 6x 2 + 3xy5x 2 – 3x – 7 4ab 3 c 2 7x – 3y3v 2 – 5w + 7z

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 8x 5 - 3x 2 + 2x – 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. The degree of 4, we will refer to as 4 th degree, the degree of 5, 5 th degree and so forth. PolynomialDegreeName -150Constant 3x – 61Linear 5x + 7 – 3x 2 2Quadratic 15x – 2y3Cubic

FULL NAME OF A POLYNOMIAL FIRST NAME: NAME USING THE DEGREE LAST NAME: NAME USING # OF TERMS PolynomialDegreeName using degree # of TermsName using # of terms Full Name 5x + 11Linear2BinomialLinear Binomial -150Constant1MonomialConstant Monomial 16x 2 - 5x + 32Quadratic3TrinomialQuadratic Trinomial 3x 4 – 744 th Degree2Binomial4 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. 7x 2 + 2x 4 – 11 B. 6x – 8x – 2x 3 2x 4 + 7x 2 – 11 -2x 3 + 6x 2 – 8x + 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.combining like termsorder of operationsconfuse Let’s take a Look at a couple of your examples *Distribute the (-) 1. (4x 2 +6x + 7) + (2x – 9x) 5. (2x 3 + 5x 2 - 3x) – (x 3 – 8x ) 2x 3 + 5x 2 – 3x –x 3 + 8x x 2 - 3x + 8 x x 2 - 3x - 11