Polynomials. Common Mistakes

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1 Polnomils

2 Polnomils Definition A polnomil is single term or sum or difference of terms in which ll vribles hve whole-number eponents nd no vrible ppers in the denomintor. Ech term cn be either constnt, vrible, or combintion of coefficients nd vribles. The numericl prt of the term is the coefficient. The highest power is the degree of the polnomil. Not polnomil: Polnomil: The coefficient of the term 6 is 6. The degree of the polnomil 5 is. 6 The coefficient of the term 6is. 6 The degree of the polnomil 5 is 5. 6 Complete Mnul:..\Polnomil Review.doc To view; right click nd open hperlink

3 Polnomils Tpes of Polnomils Monomil-A constnt, or the product of constnt, nd one or more vribles rised to whole number. Emple: 6 Polnomil-An finite sum (or difference) of terms. Emple: z 9 z z Binomil-A polnomil consisting of ectl two terms. Emple: 7 Trinomil-A polnomil consisting of ectl three terms. Emple: Complete Mnul:..\Polnomil Review.doc To view; right click nd open hperlink

4 Polnomils-Adding/Subtrcting How to Add nd Subtrct Polnomils To dd or subtrct polnomils combine like terms (group together the sme vrible terms with the sme degrees). When subtrcting, if the subtrction sign (or negtive sign) is outside of prenthesis, ou must distribute the negtive sign to ech of the terms inside the prenthesis. Addition Simplif : ( Subtrction Simplif : ( 5) ( 1 or 1 5) ( 5 6 6) 1 6) Complete Mnul:..\Polnomil Review.doc To view; right click nd open hperlink

5 Polnomils-Multipling How to Multipl Polnomils To multipl monomil b monomil multipl the coefficients together then multipl the vribles using the sme rules tht ppl s with eponents. To multipl monomil nd polnomil distribute the monomil cross the polnomil. Follow the sme rules s with multipling monomils Multipl monomils Simplif : ( 6 6 Multipl monomil nd polnomil Simplif : ( )( or ) 6)

6 Polnomils-Multipling (continued) How to Multipl Polnomils To multipl binomil b binomil multipl ech term in the first binomil b ech term in the second binomil. Use FOIL method to ssist in remembering which terms need to be multiplied with which. Combine like terms. To multipl polnomil b nother polnomil multipl ech term in the first polnomil b ech term in the second polnomil. Combine like terms. Multipl binomils Simplif : ( 5)( ) 6 10 or Multipl polnomils Simplif : ( )( 5 ) ( ( ) (5) ) (5) () ( ) (5) () Complete Mnul:..\Polnomil Review.doc To view; right click nd open hperlink

7 Polnomils-Specil Products How to Multipl Specil Products ( ( b) or ( b) b) ( b) ( b)( b) b b b b b Multipl Simplif : ( 5) 9 5 or () ()(5) (5) ( b) b b b Multipl ( b) or ( b Simplif : ( ) ) ( b) b b b 8 7 or 7 () () () ()() () Complete Mnul:..\Polnomil Review.doc To view; right click nd open hperlink

8 Polnomils-Dividing How to Divide Polnomils To divide polnomil b single term tret the division s simplifiction nd reduce ech term to the lowest terms possible. Divide b monomil Simplif : or 1 1 ) ( or 1 / / / / Complete Mnul:..\Polnomil Review.doc To view; right click nd open hperlink

9 Polnomils-Long Division How to Do Long Division of Polnomils Long division of polnomils is the sme s regulr long division, with the eception tht vribles re included. Long Division Divide 6 1 b ( 6 16) ( ) ( ) ( ) /( ) 16 8 Complete Mnul:..\Polnomil Review.doc To view; right click nd open hperlink ( ) 8 16 ( 8 16) 0 ( 16) ( ) ( 6 8)

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