Transcription of Polynomials in Two Variables - Math
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Polynomials in Two Variables - Math
Polynomials in Two VariablesAfunction in two variablesis a functionf:D!RwhereDis a subset ofthe plane, The functiong:R2!Rwhereg(x,y)=xy+3isafunctio nintwovariables. Notice thatg(1,2) = 1 2+3=5, thatg(0, 7) = 0 ( 7) + 3 = 3,and thatg(4,5) = 4 5+3=23. LetDbe the set of all vectors in the plane whosex-coordinates aregreater than or equal to 0. That is,D={(x,y)2R2|x 0}. Thenh:D!Rwhereh(x,y)=px+yis a function in two Variables . Notice thath(4,3) =p4+3=2+3=5,andthath(0, 10) = 10. The functionf:R2!Rwheref(x,y)= x2+2xy+y2 2x+3y+10is a function in two Variables . Check thatf(0,1) = 0+0+1 0+3+10 = 14and thatf(2,3) = 4+12+9 4+9+10=32. g:R2!R2whereg(x,y)=5isaconstantfunction. Theoutputofgis always 5, regardless of the in two Variables have domains that are subsets of the plane, \\\\\\\\\\\\\\\\\\\\\\PolynomialsAdegree 0 polynomial in two variablesis a function of the formp(x,y)=a0,0for some constant numbera0, example,p(x,y)=4isadegree0polynomial,and soisq(x,y)= are just constant functions, and because of that, degree 0 polynomialsare often calledconstant 1 polynomial in two variablesis a function of the formp(x,y)=a1,0x+a0,1y+a0,0wherea1,0,a0, 1,a0,02R,aslongasa1,0anda0,1don t both equal example,p(x,y)=2x+4y+5 is a degree 1 polynomial in two areq(x,y)= 2x+3,f(x,y)=y,andg(x,y)=x y.
can multiply any collection of numbers, and you can add any collection of numbers. There are no restrictions. The domain of any polynomial in two variables is the entire plane, R2. Coecients and terms If we have a polynomial such as p(x,y)=a2,0x 2 +a 1,1xy +a0,2y 2 +a 1,0x+a0,1y +a0,0 then we call a2,0x 2 the x2-term of p(x,y). Similarly, we ...
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