hola quien me hace la pagina de algebra 83 los 14 ejercicios y les doy todos mis puntos gracias
Geral05:
Lo que necesitas es el procedimiento, cierto?
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La página 83 de Álgebra de Baldor indica el ejercicio 52 con 14 incisos de División de un polinomio por un monomio:
![52)1) a^2-ab \quad entre \ a \\ \\ \frac{a^2-ab}{a}= \quad \ distribuis\ el \ denominador \\ \\ \frac{a^2 }{a}- \frac{ab}{a} = \qquad simplicas\ "a" \ y \ tu \ resultado \ es \quad \boxed{a-b} \\ \\ \frac{a^2-ab}{a}= \frac{a^2 }{a}- \frac{ab}{a} = \frac{a}{1}- \frac{b}{1}= \boxed{a-b} 52)1) a^2-ab \quad entre \ a \\ \\ \frac{a^2-ab}{a}= \quad \ distribuis\ el \ denominador \\ \\ \frac{a^2 }{a}- \frac{ab}{a} = \qquad simplicas\ "a" \ y \ tu \ resultado \ es \quad \boxed{a-b} \\ \\ \frac{a^2-ab}{a}= \frac{a^2 }{a}- \frac{ab}{a} = \frac{a}{1}- \frac{b}{1}= \boxed{a-b}](https://tex.z-dn.net/?f=52%291%29+a%5E2-ab+%5Cquad+entre+%5C+a+%5C%5C++%5C%5C++%5Cfrac%7Ba%5E2-ab%7D%7Ba%7D%3D+%5Cquad+%5C+distribuis%5C+el+%5C+denominador+++%5C%5C++%5C%5C++%5Cfrac%7Ba%5E2+%7D%7Ba%7D-+%5Cfrac%7Bab%7D%7Ba%7D++%3D+%5Cqquad+simplicas%5C+%22a%22+%5C+y+%5C+tu+%5C+resultado+%5C+es+%5Cquad++%5Cboxed%7Ba-b%7D+%5C%5C++%5C%5C+++%5Cfrac%7Ba%5E2-ab%7D%7Ba%7D%3D+%5Cfrac%7Ba%5E2+%7D%7Ba%7D-++%5Cfrac%7Bab%7D%7Ba%7D++%3D++%5Cfrac%7Ba%7D%7B1%7D-++%5Cfrac%7Bb%7D%7B1%7D%3D++%5Cboxed%7Ba-b%7D+)
![2) \frac{3x^2y^3-5a^2x^4}{-3x^2} = \frac{3x^2y^3}{-3x^2}- \frac{5a^2x^4}{-3x^2} = \boxed{-y^3+ \frac{5}{3}a^2x^2} \\ \\ \\ 3) \frac{3a^3-5ab^2-6a^2b^3}{-2a}= \frac{3a^3}{-2a}-\frac{5ab^2}{-2a}-\frac{6a^2b^3}{-2a}= \boxed{ -\frac{3}{2}a+ \frac{5}{2}b^2+3ab^3} \\ \\ \\ 4) \frac{x^3-4x^2+x}{x} = \frac{x^3}{x} - \frac{4x^2}{x} + \frac{x}{x} = \boxed{x^2-4x+1} \\ \\ \\ 5) \frac{4x^8-10x^6+5x^4}{2x^3} = \frac{4x^8}{2x^3}- \frac{10x^6}{2x^3}+\frac{5x^4}{2x^3} = \boxed{x^5-5x^3+ \frac{5}{2} x} 2) \frac{3x^2y^3-5a^2x^4}{-3x^2} = \frac{3x^2y^3}{-3x^2}- \frac{5a^2x^4}{-3x^2} = \boxed{-y^3+ \frac{5}{3}a^2x^2} \\ \\ \\ 3) \frac{3a^3-5ab^2-6a^2b^3}{-2a}= \frac{3a^3}{-2a}-\frac{5ab^2}{-2a}-\frac{6a^2b^3}{-2a}= \boxed{ -\frac{3}{2}a+ \frac{5}{2}b^2+3ab^3} \\ \\ \\ 4) \frac{x^3-4x^2+x}{x} = \frac{x^3}{x} - \frac{4x^2}{x} + \frac{x}{x} = \boxed{x^2-4x+1} \\ \\ \\ 5) \frac{4x^8-10x^6+5x^4}{2x^3} = \frac{4x^8}{2x^3}- \frac{10x^6}{2x^3}+\frac{5x^4}{2x^3} = \boxed{x^5-5x^3+ \frac{5}{2} x}](https://tex.z-dn.net/?f=2%29++%5Cfrac%7B3x%5E2y%5E3-5a%5E2x%5E4%7D%7B-3x%5E2%7D+%3D+%5Cfrac%7B3x%5E2y%5E3%7D%7B-3x%5E2%7D-+%5Cfrac%7B5a%5E2x%5E4%7D%7B-3x%5E2%7D+%3D++%5Cboxed%7B-y%5E3%2B+%5Cfrac%7B5%7D%7B3%7Da%5E2x%5E2%7D++%5C%5C++%5C%5C++%5C%5C+3%29++%5Cfrac%7B3a%5E3-5ab%5E2-6a%5E2b%5E3%7D%7B-2a%7D%3D++%5Cfrac%7B3a%5E3%7D%7B-2a%7D-%5Cfrac%7B5ab%5E2%7D%7B-2a%7D-%5Cfrac%7B6a%5E2b%5E3%7D%7B-2a%7D%3D+%5Cboxed%7B+-%5Cfrac%7B3%7D%7B2%7Da%2B+%5Cfrac%7B5%7D%7B2%7Db%5E2%2B3ab%5E3%7D++%5C%5C++%5C%5C++%5C%5C+4%29++%5Cfrac%7Bx%5E3-4x%5E2%2Bx%7D%7Bx%7D+%3D++%5Cfrac%7Bx%5E3%7D%7Bx%7D+-+%5Cfrac%7B4x%5E2%7D%7Bx%7D+%2B+%5Cfrac%7Bx%7D%7Bx%7D+%3D+%5Cboxed%7Bx%5E2-4x%2B1%7D+++%5C%5C++%5C%5C++%5C%5C+5%29++%5Cfrac%7B4x%5E8-10x%5E6%2B5x%5E4%7D%7B2x%5E3%7D+%3D+%5Cfrac%7B4x%5E8%7D%7B2x%5E3%7D-+%5Cfrac%7B10x%5E6%7D%7B2x%5E3%7D%2B%5Cfrac%7B5x%5E4%7D%7B2x%5E3%7D+%3D+++%5Cboxed%7Bx%5E5-5x%5E3%2B+%5Cfrac%7B5%7D%7B2%7D+x%7D++)
![6) \frac{6m^3-8m^2n+20mn}{-2m}= \frac{6m^3}{-2m}- \frac{8m^2n}{-2m}+ \frac{20mn}{-2m}= \boxed{-3m^2+4mn-10n} \\ \\ 7) \frac{6a^8b^8-3a^6b^6-a^2b^3}{3a^2b^3}= \frac{6a^8b^8}{3a^2b^3}- \frac{3a^6b^6}{3a^2b^3}- \frac{a^2b^3}{3a^2b^3}= \boxed{2a^6b^5-a^4b^3- \frac{1}{3} } \\ \\ 8) \frac{x^4-5x^3-10x^2+15x}{-5x}= \frac{x^4}{-5x}- \frac{5x^3}{-5x}- \frac{10x^2}{-5x}+ \frac{15x}{-5x}= \boxed{ -\frac{1}{5} x^3+x^2+2x-3} 6) \frac{6m^3-8m^2n+20mn}{-2m}= \frac{6m^3}{-2m}- \frac{8m^2n}{-2m}+ \frac{20mn}{-2m}= \boxed{-3m^2+4mn-10n} \\ \\ 7) \frac{6a^8b^8-3a^6b^6-a^2b^3}{3a^2b^3}= \frac{6a^8b^8}{3a^2b^3}- \frac{3a^6b^6}{3a^2b^3}- \frac{a^2b^3}{3a^2b^3}= \boxed{2a^6b^5-a^4b^3- \frac{1}{3} } \\ \\ 8) \frac{x^4-5x^3-10x^2+15x}{-5x}= \frac{x^4}{-5x}- \frac{5x^3}{-5x}- \frac{10x^2}{-5x}+ \frac{15x}{-5x}= \boxed{ -\frac{1}{5} x^3+x^2+2x-3}](https://tex.z-dn.net/?f=6%29++%5Cfrac%7B6m%5E3-8m%5E2n%2B20mn%7D%7B-2m%7D%3D++%5Cfrac%7B6m%5E3%7D%7B-2m%7D-+%5Cfrac%7B8m%5E2n%7D%7B-2m%7D%2B++%5Cfrac%7B20mn%7D%7B-2m%7D%3D++%5Cboxed%7B-3m%5E2%2B4mn-10n%7D+%5C%5C++%5C%5C+7%29+%5Cfrac%7B6a%5E8b%5E8-3a%5E6b%5E6-a%5E2b%5E3%7D%7B3a%5E2b%5E3%7D%3D+%5Cfrac%7B6a%5E8b%5E8%7D%7B3a%5E2b%5E3%7D-+%5Cfrac%7B3a%5E6b%5E6%7D%7B3a%5E2b%5E3%7D-+%5Cfrac%7Ba%5E2b%5E3%7D%7B3a%5E2b%5E3%7D%3D++%5Cboxed%7B2a%5E6b%5E5-a%5E4b%5E3-+%5Cfrac%7B1%7D%7B3%7D+%7D++%5C%5C++%5C%5C+8%29+%5Cfrac%7Bx%5E4-5x%5E3-10x%5E2%2B15x%7D%7B-5x%7D%3D++%5Cfrac%7Bx%5E4%7D%7B-5x%7D-+%5Cfrac%7B5x%5E3%7D%7B-5x%7D-+%5Cfrac%7B10x%5E2%7D%7B-5x%7D%2B+%5Cfrac%7B15x%7D%7B-5x%7D%3D+%5Cboxed%7B+-%5Cfrac%7B1%7D%7B5%7D+x%5E3%2Bx%5E2%2B2x-3%7D+)
![9) \frac{8m^9n^2-10m^7n^4-20m^5n^6+12m^3n^8}{2m^2}= \\ \\ \frac{8m^9n^2}{2m^2}-\frac{10m^7n^4}{2m^2}-\frac{20m^5n^6}{2m^2}+\frac{12m^3n^8}{2m^2}= \\ \\ \boxed{4m^7n^2-5m^5n^4-10m^3n^6+6mn^8} \\ \\ 10) \frac{a^x+a^{m-1} }{a^2}= \frac{a^x }{a^2}+ \frac{a^{m-1} }{a^2}= a^{x-2}+a^{m-1-2}= \boxed{a^{x-2}+a^{m-3}} \\ \\ 9) \frac{8m^9n^2-10m^7n^4-20m^5n^6+12m^3n^8}{2m^2}= \\ \\ \frac{8m^9n^2}{2m^2}-\frac{10m^7n^4}{2m^2}-\frac{20m^5n^6}{2m^2}+\frac{12m^3n^8}{2m^2}= \\ \\ \boxed{4m^7n^2-5m^5n^4-10m^3n^6+6mn^8} \\ \\ 10) \frac{a^x+a^{m-1} }{a^2}= \frac{a^x }{a^2}+ \frac{a^{m-1} }{a^2}= a^{x-2}+a^{m-1-2}= \boxed{a^{x-2}+a^{m-3}} \\ \\](https://tex.z-dn.net/?f=9%29+%5Cfrac%7B8m%5E9n%5E2-10m%5E7n%5E4-20m%5E5n%5E6%2B12m%5E3n%5E8%7D%7B2m%5E2%7D%3D+%5C%5C++%5C%5C+%5Cfrac%7B8m%5E9n%5E2%7D%7B2m%5E2%7D-%5Cfrac%7B10m%5E7n%5E4%7D%7B2m%5E2%7D-%5Cfrac%7B20m%5E5n%5E6%7D%7B2m%5E2%7D%2B%5Cfrac%7B12m%5E3n%5E8%7D%7B2m%5E2%7D%3D++%5C%5C++%5C%5C+%5Cboxed%7B4m%5E7n%5E2-5m%5E5n%5E4-10m%5E3n%5E6%2B6mn%5E8%7D++%5C%5C++%5C%5C+10%29++%5Cfrac%7Ba%5Ex%2Ba%5E%7Bm-1%7D+%7D%7Ba%5E2%7D%3D++%5Cfrac%7Ba%5Ex+%7D%7Ba%5E2%7D%2B+%5Cfrac%7Ba%5E%7Bm-1%7D+%7D%7Ba%5E2%7D%3D+a%5E%7Bx-2%7D%2Ba%5E%7Bm-1-2%7D%3D+%5Cboxed%7Ba%5E%7Bx-2%7D%2Ba%5E%7Bm-3%7D%7D++%5C%5C++%5C%5C+++)
![11) \frac{2a^m-3a ^{m+2} +6a^{m+4} }{-3a^3}= \frac{2a^m }{-3a^3}- \frac{3a ^{m+2} }{-3a^3}+ \frac{6a^{m+4} }{-3a^3}= \\ \\ - \frac{2}{3}a ^{m-3}+a^{m+2-3}-2 a^{m+4-3}= \boxed{- \frac{2}{3}a ^{m-3}+a^{m-1}-2 a^{m+1}} \\ \\ 11) \frac{2a^m-3a ^{m+2} +6a^{m+4} }{-3a^3}= \frac{2a^m }{-3a^3}- \frac{3a ^{m+2} }{-3a^3}+ \frac{6a^{m+4} }{-3a^3}= \\ \\ - \frac{2}{3}a ^{m-3}+a^{m+2-3}-2 a^{m+4-3}= \boxed{- \frac{2}{3}a ^{m-3}+a^{m-1}-2 a^{m+1}} \\ \\](https://tex.z-dn.net/?f=11%29++%5Cfrac%7B2a%5Em-3a+%5E%7Bm%2B2%7D+%2B6a%5E%7Bm%2B4%7D+%7D%7B-3a%5E3%7D%3D+++%5Cfrac%7B2a%5Em+%7D%7B-3a%5E3%7D-+++%5Cfrac%7B3a+%5E%7Bm%2B2%7D+%7D%7B-3a%5E3%7D%2B+%5Cfrac%7B6a%5E%7Bm%2B4%7D+%7D%7B-3a%5E3%7D%3D+++%5C%5C++%5C%5C++-+%5Cfrac%7B2%7D%7B3%7Da+%5E%7Bm-3%7D%2Ba%5E%7Bm%2B2-3%7D-2+a%5E%7Bm%2B4-3%7D%3D++%5Cboxed%7B-+%5Cfrac%7B2%7D%7B3%7Da+%5E%7Bm-3%7D%2Ba%5E%7Bm-1%7D-2+a%5E%7Bm%2B1%7D%7D++%5C%5C++%5C%5C+++)
![12) \frac{a^mb^n+a ^{m-1}b^{n+2} -a^{m-2}b^{n+4} }{a^2b^3}= \\ \\ \frac{a^mb^n }{a^2b^3}+ \frac{a ^{m-1}b^{n+2} }{a^2b^3}-\frac{a^{m-2}b^{n+4} }{a^2b^3}= \\ \\ a^{m-2}b^{n-3}+a ^{m-1-2}b^{n+2-3} -a^{m-2-2}b^{n+4-3}= \\ \\ \boxed{a^{m-2}b^{n-3}+a ^{m-3}b^{n-1} -a^{m-4}b^{n+1} } 12) \frac{a^mb^n+a ^{m-1}b^{n+2} -a^{m-2}b^{n+4} }{a^2b^3}= \\ \\ \frac{a^mb^n }{a^2b^3}+ \frac{a ^{m-1}b^{n+2} }{a^2b^3}-\frac{a^{m-2}b^{n+4} }{a^2b^3}= \\ \\ a^{m-2}b^{n-3}+a ^{m-1-2}b^{n+2-3} -a^{m-2-2}b^{n+4-3}= \\ \\ \boxed{a^{m-2}b^{n-3}+a ^{m-3}b^{n-1} -a^{m-4}b^{n+1} }](https://tex.z-dn.net/?f=12%29++%5Cfrac%7Ba%5Emb%5En%2Ba+%5E%7Bm-1%7Db%5E%7Bn%2B2%7D+-a%5E%7Bm-2%7Db%5E%7Bn%2B4%7D++%7D%7Ba%5E2b%5E3%7D%3D++++%5C%5C++%5C%5C+%5Cfrac%7Ba%5Emb%5En+%7D%7Ba%5E2b%5E3%7D%2B+%5Cfrac%7Ba+%5E%7Bm-1%7Db%5E%7Bn%2B2%7D++%7D%7Ba%5E2b%5E3%7D-%5Cfrac%7Ba%5E%7Bm-2%7Db%5E%7Bn%2B4%7D++%7D%7Ba%5E2b%5E3%7D%3D++%5C%5C++%5C%5C+a%5E%7Bm-2%7Db%5E%7Bn-3%7D%2Ba+%5E%7Bm-1-2%7Db%5E%7Bn%2B2-3%7D+-a%5E%7Bm-2-2%7Db%5E%7Bn%2B4-3%7D%3D+++%5C%5C++%5C%5C++%5Cboxed%7Ba%5E%7Bm-2%7Db%5E%7Bn-3%7D%2Ba+%5E%7Bm-3%7Db%5E%7Bn-1%7D+-a%5E%7Bm-4%7Db%5E%7Bn%2B1%7D+%7D+++++++++)
![13) \frac{x ^{m+2} -5x^{m} +6x^{m+1}<span>-x</span>^{m-1}}{x^{m-2}}= \\ \\ \frac{x ^{m+2} }{x^{m-2}}- \frac{5x^{m}}{x^{m-2}}+ \frac{6x^{m+1}}{x^{m-2}} -\frac{x^{m-1}}{x^{m-2}} =\\ \\ x^{(m+2)-(m-2)}-5x^{m-(m-2)}+6x^{(m+1)-(m-2)}-x^{(m-1)-(m-2)}= \\ \\ x^{m+2-m+2}-5x^{m-m+2}+6x^{m+1-m+2}-x^{m-1-m+2}= \\ \\ x^{4}-5x^{2}+6x^{3}-x^{1}= \boxed{x^{4}-5x^{2}+6x^{3}-x} \\ \\ 13) \frac{x ^{m+2} -5x^{m} +6x^{m+1}<span>-x</span>^{m-1}}{x^{m-2}}= \\ \\ \frac{x ^{m+2} }{x^{m-2}}- \frac{5x^{m}}{x^{m-2}}+ \frac{6x^{m+1}}{x^{m-2}} -\frac{x^{m-1}}{x^{m-2}} =\\ \\ x^{(m+2)-(m-2)}-5x^{m-(m-2)}+6x^{(m+1)-(m-2)}-x^{(m-1)-(m-2)}= \\ \\ x^{m+2-m+2}-5x^{m-m+2}+6x^{m+1-m+2}-x^{m-1-m+2}= \\ \\ x^{4}-5x^{2}+6x^{3}-x^{1}= \boxed{x^{4}-5x^{2}+6x^{3}-x} \\ \\](https://tex.z-dn.net/?f=13%29+%5Cfrac%7Bx+%5E%7Bm%2B2%7D+-5x%5E%7Bm%7D+%2B6x%5E%7Bm%2B1%7D%3Cspan%3E-x%3C%2Fspan%3E%5E%7Bm-1%7D%7D%7Bx%5E%7Bm-2%7D%7D%3D+%5C%5C++%5C%5C++%5Cfrac%7Bx+%5E%7Bm%2B2%7D+%7D%7Bx%5E%7Bm-2%7D%7D-+%5Cfrac%7B5x%5E%7Bm%7D%7D%7Bx%5E%7Bm-2%7D%7D%2B+%5Cfrac%7B6x%5E%7Bm%2B1%7D%7D%7Bx%5E%7Bm-2%7D%7D+-%5Cfrac%7Bx%5E%7Bm-1%7D%7D%7Bx%5E%7Bm-2%7D%7D+%3D%5C%5C++%5C%5C+x%5E%7B%28m%2B2%29-%28m-2%29%7D-5x%5E%7Bm-%28m-2%29%7D%2B6x%5E%7B%28m%2B1%29-%28m-2%29%7D-x%5E%7B%28m-1%29-%28m-2%29%7D%3D+%5C%5C++%5C%5C+x%5E%7Bm%2B2-m%2B2%7D-5x%5E%7Bm-m%2B2%7D%2B6x%5E%7Bm%2B1-m%2B2%7D-x%5E%7Bm-1-m%2B2%7D%3D+%5C%5C++%5C%5C++x%5E%7B4%7D-5x%5E%7B2%7D%2B6x%5E%7B3%7D-x%5E%7B1%7D%3D+%5Cboxed%7Bx%5E%7B4%7D-5x%5E%7B2%7D%2B6x%5E%7B3%7D-x%7D++%5C%5C++%5C%5C++++++++)
![14) \frac{4a ^{x+4} b^{m-1} -6a^{x+3}b^{m-1}+8a^{x+2}b^{m-3} }{-2a^{x+2} b^{m-4} }= \\ \\ \frac{4a ^{x+4} b^{m-1} }{-2a^{x+2} b^{m-4} }-\frac{6a^{x+3}b^{m-1} }{-2a^{x+2} b^{m-4} }+\frac{8a^{x+2}b^{m-3} }{-2a^{x+2} b^{m-4} }= \\ \\-2a ^{(x+4)-(x+2)} b^{(m-1)-(m-4)}}- 3a^{(x+3)-(x+2)}b^{(m-1)-(m-4)} \\ 8a^{(x+2)-(x+2)}b^{(m-3)-(m-4)}= \\ \\ \boxed{-2a ^{2} b^{3}- 3a^{1}b^{3}+ 8a^{0}b^{1}\to-2a^2b^3-3ab^3+8b} 14) \frac{4a ^{x+4} b^{m-1} -6a^{x+3}b^{m-1}+8a^{x+2}b^{m-3} }{-2a^{x+2} b^{m-4} }= \\ \\ \frac{4a ^{x+4} b^{m-1} }{-2a^{x+2} b^{m-4} }-\frac{6a^{x+3}b^{m-1} }{-2a^{x+2} b^{m-4} }+\frac{8a^{x+2}b^{m-3} }{-2a^{x+2} b^{m-4} }= \\ \\-2a ^{(x+4)-(x+2)} b^{(m-1)-(m-4)}}- 3a^{(x+3)-(x+2)}b^{(m-1)-(m-4)} \\ 8a^{(x+2)-(x+2)}b^{(m-3)-(m-4)}= \\ \\ \boxed{-2a ^{2} b^{3}- 3a^{1}b^{3}+ 8a^{0}b^{1}\to-2a^2b^3-3ab^3+8b}](https://tex.z-dn.net/?f=14%29+%5Cfrac%7B4a+%5E%7Bx%2B4%7D+b%5E%7Bm-1%7D+-6a%5E%7Bx%2B3%7Db%5E%7Bm-1%7D%2B8a%5E%7Bx%2B2%7Db%5E%7Bm-3%7D+%7D%7B-2a%5E%7Bx%2B2%7D+b%5E%7Bm-4%7D+%7D%3D++%5C%5C++%5C%5C+%5Cfrac%7B4a+%5E%7Bx%2B4%7D+b%5E%7Bm-1%7D+%7D%7B-2a%5E%7Bx%2B2%7D+b%5E%7Bm-4%7D+%7D-%5Cfrac%7B6a%5E%7Bx%2B3%7Db%5E%7Bm-1%7D+%7D%7B-2a%5E%7Bx%2B2%7D+b%5E%7Bm-4%7D+%7D%2B%5Cfrac%7B8a%5E%7Bx%2B2%7Db%5E%7Bm-3%7D+%7D%7B-2a%5E%7Bx%2B2%7D+b%5E%7Bm-4%7D+%7D%3D+%5C%5C++%5C%5C-2a+%5E%7B%28x%2B4%29-%28x%2B2%29%7D+b%5E%7B%28m-1%29-%28m-4%29%7D%7D-+3a%5E%7B%28x%2B3%29-%28x%2B2%29%7Db%5E%7B%28m-1%29-%28m-4%29%7D++%5C%5C+8a%5E%7B%28x%2B2%29-%28x%2B2%29%7Db%5E%7B%28m-3%29-%28m-4%29%7D%3D+%5C%5C++%5C%5C+%5Cboxed%7B-2a+%5E%7B2%7D+b%5E%7B3%7D-+3a%5E%7B1%7Db%5E%7B3%7D%2B+8a%5E%7B0%7Db%5E%7B1%7D%5Cto-2a%5E2b%5E3-3ab%5E3%2B8b%7D+)
Espero que te sirva, salu2!!!!
Espero que te sirva, salu2!!!!
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