Polynomials a variable expression whose terms are Monomials. - PowerPoint PPT Presentation

D AY 131 – P OLYNOMIAL O PERATIONS

V OCABULARY Monomial – a Number, a Variable or a PRODUCT of a number and a variable. * monomials cannot have radicals with variables inside, quotients of variables or variables with negative exponents. Degree of a monomial – is the SUM of the exponents of the variable(s) in the monomial. The degree of constant term is 0.

Polynomials – a variable expression whose terms are Monomials. Monomials have 1 term. Binomials have 2 terms. Trinomials have 3 terms. Polynomials with more than 3 terms do not have special names. Polynomials in one variable are usually arranged in descending order so that the exponents of the variables decrease from left to right. *polynomials(just like monomials) cannot have radicals with variables inside, quotients of variables or variables with negative exponents.

Degree of polynomial – is the Greatest of the degrees of any of its terms. (Remember each term is a monomial so the degree will be the sum of the exponents in the monomial.) Constant Term of Polynomial – Term that does not have a variable attached to it. Leading Coefficient of Polynomial – is the coefficient of the variable with the largest exponent.

Evaluate Polynomials – just substitute in the assigned value for the variable and find the value of the polynomial.    Example: The value will be 45. 3 2 4 6 evaluate 3 . x x x    2 3 ( 3 ) 4 ( 3 ) 6 45 .

Add Polynomials – to add polynomials just Combine like terms. There are 2 formats you can use to add polynomials – horizontal format or vertical format. Example: Horizontal Format:         2 2 2 ( 3 4 6 ) ( 7 2 2 ) 10 6 4 x x x x x x Vertical Format  x  2 ( 3 4 6 ) x    2 ( 7 2 2 ) x x  x  10 2 6 4 x

Subtract Polynomials – To subtract polynomials just Add the additive inverse of the 2 nd polynomial. There are 2 formats you can use to subtract polynomials – horizontal format or vertical format. Example: Horizontal Format:          2 2 2 ( 3 4 6 ) ( 7 2 2 ) 4 2 8 x x x x x x Vertical Format  x  2 ( 3 4 6 ) x    2 ( 7 2 2 ) x x    2 4 2 8 x x

I N EACH PYRAMID EACH BLOCK IS THE SUM OF THE TWO BLOCKS BELOW . F ILL IN THE MISSING EXPRESSIONS . 1. 2.

I N EACH PYRAMID EACH BLOCK IS THE SUM OF THE TWO BLOCKS BELOW . F ILL IN THE MISSING EXPRESSIONS . 1. 2.

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