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# 478 Note 6 for MA 15200 at Purdue

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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Purdue University taught by a professor in Fall. Since its upload, it has received 19 views.

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Date Created: 02/06/15

MA 15200 Lesson 6 Section PA I Polynomials A Monomial or Term is a number or the product of a number and one or more variables with wholenumber exponents The number factor is called a Coef cient of the term The Degree of the monomial or term is the sum of the exponents of it variables A Constant has degree 0 Ex 1 For each term state the coef cient and the degree of the term a 14x3y b a5 7139 2 c 7r h 2 d 51 A monomial or a sum of monomials is called a Polvnomial A polvnomial with 2 terms is called a Binomial and a polvnomial with 3 terms is called a Trinomial Ex 2 For each polynomial state the number of terms a 4x3 5x 9x4 3x2 b 12x2y 7x2y2 8992 The Degree of the Polvnomial is the degree of the term that has the highest degree The leading coef cient of a polynomial is the coef cient of the term with the highest degree That term is also called the leading term Ex 3 For each polynomial state the degree the leading coefficient and the leading term a 4x3 3x4 2x 3x2 3 b 4a 102a3 7a2 5614 A polynomial of one variable is written in standard form when the terms are written in the order of descending powers of the variable Ex 4 Write each polynomial is example 3 in standard form 11 Addition and Subtraction of Polynomials Polynomials are added or subtracted by combining like terms The answers if possible are usually given in standard form Some students nd addition or subtraction easier if the polynomials are aligned vertically AdditionSubtraction 0f Polvnomials To add or subtract polynomials 1 Remove parentheses using the distributive property 2 Combine any like terms EX 5 Add Subtract these polynomials a 3613b 7612b 4ab 5612b l4a3b 8ab b 4x3 4x2x2 6 2x2 9 3x x3 c 42m3 7m268m2 m3 22m3 3m2 d 4m2n 3mn 5n2 3mn 8m2n n2 7n2 2mm III Multiplication of Polynomials Multiplication of Polynomials 1 To multiply two monomials Use regular rules of eXponents39 Multiply the coefficients and multiply the variables 2 To multiply a monomial and a polynomial binomial or more terms Use the distributive property Multiply each term of the polynomial by the monomial 3 To multiply two binomials Use FOIL rst outer inner last 4 To multiply two general polynomials with 2 or more terms Multiply each term of one polynomial by each term of the other polynomial Then combine like terms There is a good tip about the difference between addition and multiplication of monomials on page 51 0f the text EX 6 Multiply and write product in simpli ed form a 4a2b ab4 b 4xy23x3 2x2y xyz c m23m 5 d 2yx5y 2x e 4x3x2 3x4 f 4612 62a3 Note Only two polynomials other than monomials can be multiplied at one time To nd the following product multiply two of the binomials then multiply that product by the third binomial m x 3x 42x 1 Special Products 1 Product of a Sum and Difference of two terms 2 x yx y x2 y These types of binomials are called conjugates The Square of a Binomial 2 xy2 x2 2xyy2 1st2 21st2nd 2nd2 3 x y2 x2 2gvy2 1st2 2lst2nd 2nd2 See the study Tip of page 54 of the text The mistake shown is very common with students EX 8 Find each product in simplest form a 4m 3112 b 6 5w6 SW c 6 7n2 d 6a 2b6a 2b EX9 The volume of a box is V Lwh Find a polynomial to represent the volume of the box below 2xl4 9

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