9-1: adding and subtracting polynomials · 2019. 3. 1. · 9-1: adding and subtracting polynomials...

9-1: ADDING AND SUBTRACTING POLYNOMIALS Lesson Objectives: • Classify polynomials • Add and subtract polynomials A monomial is an expression that is a number, a variable, or a product of a number and one or more variables. The degree of a monomial is the sum of the exponents of its variables. For a nonzero constant, the degree is 0. Zero has no degree. EXAMPLE 1: DEGREE OF A MONOMIAL Find the degree of each monomial. 1. 3xy 3 2. 18 3. 5m 4. 4 x 5 EXAMPLE 2: CLASSIFYING POLYNOMIALS A polynomial is a monomial or the sum or difference of two or more monomials. 3x 4 + 5x 2 − 7 x + 1 The polynomial shown above is in standard form. Standard form of a polynomial means that the degrees of its monomial terms decrease from left to right. The degree of a polynomial in one variable is the same as the degree of the monomial with the greatest exponent. The degree of 3x 4 + 5x 2 − 7 x + 1 is 4. After you simplify a polynomial by combining like terms, you can name the polynomial based on its degree of the number of monomials it contains. Polynomial Degree Name Using Degree Number of Terms Name Using Number of Terms 5 7 x + 4 3x 2 + 2 x + 1 4 x 3 9 x 4 + 11x 3x 4 + 5x 2 − 7 x + 1 s 4b 4 O 1 variable in the denominator so notamonomia 0 Constant 1 monomial 1 linear 2 binomial 2 quadratic 3 trinomial 3 cubic 1 monomial 4 4th degree 2 binomial 4 4th degree 4 polynomial of 4 terms

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9-1:ADDINGANDSUBTRACTINGPOLYNOMIALS

LessonObjectives:• Classifypolynomials• Addandsubtractpolynomials

Amonomialisanexpressionthatisanumber,avariable,oraproductofanumberandoneormorevariables.Thedegreeofamonomialisthesumoftheexponentsofitsvariables.Foranonzeroconstant,thedegreeis0.Zerohasnodegree.EXAMPLE1:DEGREEOFAMONOMIALFindthedegreeofeachmonomial.1.3xy3 2.18 3.5m 4. 4x5 EXAMPLE2:CLASSIFYINGPOLYNOMIALSApolynomialisamonomialorthesumordifferenceoftwoormoremonomials. 3x4 + 5x2 − 7x +1 Thepolynomialshownaboveisinstandardform.Standardformofapolynomialmeansthatthedegreesofitsmonomialtermsdecreasefromlefttoright.Thedegreeofapolynomialinonevariableisthesameasthedegreeofthemonomialwiththegreatestexponent.Thedegreeof3x4 + 5x2 − 7x +1 is4.Afteryousimplifyapolynomialbycombiningliketerms,youcannamethepolynomialbasedonitsdegreeofthenumberofmonomialsitcontains.

Polynomial Degree NameUsingDegree

NumberofTerms NameUsingNumberofTerms

5 7x + 4

3x2 + 2x +1 4x3

9x4 +11x 3x4 + 5x2 − 7x +1

s4b

4 O 1 variableinthedenominator

sonotamonomia

0 Constant 1 monomial1 linear 2 binomial2 quadratic 3 trinomial3 cubic 1 monomial4 4thdegree 2 binomial4 4thdegree 4 polynomialof4terms
Writeeachpolynomialinstandardform.Thennameeachpolynomialbyitsdegreeandthenumberofitsterms.5.−2+ 7x 6.3x5 − 2− 2x5 + 7x 7.6x2 + 7− 9x4 8.3y− 4− y3 9.8+ 7v−11v

EXAMPLE3:ADDINGPOLYNOMIALSSimplify.10. 6x2 +3x + 7( )+ 2x2 − 6x − 4( ) 11. 12m2 + 4( )+ 8m2 + 5( ) 12. t2 − 6( )+ 3t2 +11( ) 13. 9w3 +8w2( )+ 7w3 + 4( ) 14. 2p3 − 6p2 +10p( )+ −9p3 −11p2 +3p( ) EXAMPLE4:SUBTRACTINGPOLYNOMIALSSimplify.15. 2x3 + 4x2 = 6( )− 5x3 + 2x − 2( ) 16. v3 + 6v2 − v( )− 9v3 − 7v2 +3v( )

7 2 It x 2 9 4 6 77linearbinomial 5thdegreetrinomial 4thdegreetrinomial

y3t3y 4 4vt8cubictrinomial linearbinomial

8 2 3 3 20M't9 4 2 5

16W't8W2t4 7ps I p2tBp

I2314 7 61 53 2x 3t6v2 tf9r3t7P3V3 3 4 2 2 1 8 gPtBv24V
17. 30d3 − 29d 2 −3d( )− 2d3 + d 2( ) 18. y3 +3y−1( )− y3 +3y+ 5( ) 19. 4x2 + 5x +1( )− 6x2 + x +8( ) 20. 3x + x2 − x3( )− x3 + 2x2 + 5x( ) 21. 2x2 +3− x( )− 2+ 2x2 − 5x( ) 22. 5x4 −3x3 + 2x2 + x −1( )− 3x4 −3x3 − 2x2 +3x + 7( ) 23. 2x +3( )− x − 4( )+ x + 2( ) 24. x2 + 4( )− x − 4( )+ x2 − 2x( )

3od229d23dtf2d3 d y3t3y I 1Cy 3gS281330123d 6

4 75 1 62 x 8 3 1,2 3 43 2 2 SX2 2 4 7 2 2 2 2x

2213 x C2 21754 54 37257X 1 34 3 7223 7

4 11 2 4 4 2 2x 8

2112 1714 112 It t 1 122 9 2 2 3 8