How to factor out $5^x$ from $5^x+3$?

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I know this is basic but I am having some confusion here. I need to write $5^x+5^x+3$ as $A times 5^x$. I see on khanacademy and symbolab that I am supposed to factor out $5^x$ as it is a common factor however i don't understand how $5^x$ is a common factor of $5^3$. Any understanding would be appreciated, thanks




algebra-precalculus factoring




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  • It's $5^x(1+5^3)$, if you take$5^x$ as common from the given expression.
    – Anik Bhowmick
    Aug 2 at 13:36






  • 1




    "i don't understand how $5^x$ is a common factor of $5^3$." What you really must understand is that $5^x$ is a common factor of $5^x$ and $5^x+3$.
    – drhab
    Aug 2 at 13:40














up vote
-1
down vote

favorite












I know this is basic but I am having some confusion here. I need to write $5^x+5^x+3$ as $A times 5^x$. I see on khanacademy and symbolab that I am supposed to factor out $5^x$ as it is a common factor however i don't understand how $5^x$ is a common factor of $5^3$. Any understanding would be appreciated, thanks




algebra-precalculus factoring




share|cite|improve this question





















  • It's $5^x(1+5^3)$, if you take$5^x$ as common from the given expression.
    – Anik Bhowmick
    Aug 2 at 13:36






  • 1




    "i don't understand how $5^x$ is a common factor of $5^3$." What you really must understand is that $5^x$ is a common factor of $5^x$ and $5^x+3$.
    – drhab
    Aug 2 at 13:40












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











I know this is basic but I am having some confusion here. I need to write $5^x+5^x+3$ as $A times 5^x$. I see on khanacademy and symbolab that I am supposed to factor out $5^x$ as it is a common factor however i don't understand how $5^x$ is a common factor of $5^3$. Any understanding would be appreciated, thanks




algebra-precalculus factoring




share|cite|improve this question













I know this is basic but I am having some confusion here. I need to write $5^x+5^x+3$ as $A times 5^x$. I see on khanacademy and symbolab that I am supposed to factor out $5^x$ as it is a common factor however i don't understand how $5^x$ is a common factor of $5^3$. Any understanding would be appreciated, thanks





algebra-precalculus factoring





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 2 at 13:32







user223391
















asked Aug 2 at 13:29









Sam Kha

42




42











  • It's $5^x(1+5^3)$, if you take$5^x$ as common from the given expression.
    – Anik Bhowmick
    Aug 2 at 13:36






  • 1




    "i don't understand how $5^x$ is a common factor of $5^3$." What you really must understand is that $5^x$ is a common factor of $5^x$ and $5^x+3$.
    – drhab
    Aug 2 at 13:40
















  • It's $5^x(1+5^3)$, if you take$5^x$ as common from the given expression.
    – Anik Bhowmick
    Aug 2 at 13:36






  • 1




    "i don't understand how $5^x$ is a common factor of $5^3$." What you really must understand is that $5^x$ is a common factor of $5^x$ and $5^x+3$.
    – drhab
    Aug 2 at 13:40















It's $5^x(1+5^3)$, if you take$5^x$ as common from the given expression.
– Anik Bhowmick
Aug 2 at 13:36




It's $5^x(1+5^3)$, if you take$5^x$ as common from the given expression.
– Anik Bhowmick
Aug 2 at 13:36




1




1




"i don't understand how $5^x$ is a common factor of $5^3$." What you really must understand is that $5^x$ is a common factor of $5^x$ and $5^x+3$.
– drhab
Aug 2 at 13:40




"i don't understand how $5^x$ is a common factor of $5^3$." What you really must understand is that $5^x$ is a common factor of $5^x$ and $5^x+3$.
– drhab
Aug 2 at 13:40










3 Answers
3






active

oldest

votes

















up vote
4
down vote













Hint: recall that $5^x+3=5^x cdot 5^3$. Can you take it from here?






share|cite|improve this answer





















  • Hello, thanks for the speedy response. I see how to factor 5^x from 5^x+3 however i don't understand how to obtain the answer 5^x x 126. I have 5^x + (5^x x 125). how can i simplify further from this stage?
    – Sam Kha
    Aug 2 at 13:42






  • 1




    @SamKha Use the fact that $a + bcdot a = (1+b)cdot a$
    – 5xum
    Aug 2 at 13:47






  • 1




    Sorry to see you withdraw from the moderator election, Zachary. I hope you'll reconsider.
    – Gerry Myerson
    Aug 3 at 2:42

















up vote
1
down vote













We have



$$5^x+5^x+3=5^x+5^xcdot 5^3=5^x(1+125)=126cdot 5^x$$






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    up vote
    0
    down vote













    Using index laws,
    $$5^x + 3 = 5^x cdot 5^3 = 125 cdot 5^x.$$



    Note that this is different from the situation $5^x + 5^3$, where $5^x$ would indeed have to be a factor of $5^3$ in order to (cleanly) take it out as a divisor.






    share|cite|improve this answer





















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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      4
      down vote













      Hint: recall that $5^x+3=5^x cdot 5^3$. Can you take it from here?






      share|cite|improve this answer





















      • Hello, thanks for the speedy response. I see how to factor 5^x from 5^x+3 however i don't understand how to obtain the answer 5^x x 126. I have 5^x + (5^x x 125). how can i simplify further from this stage?
        – Sam Kha
        Aug 2 at 13:42






      • 1




        @SamKha Use the fact that $a + bcdot a = (1+b)cdot a$
        – 5xum
        Aug 2 at 13:47






      • 1




        Sorry to see you withdraw from the moderator election, Zachary. I hope you'll reconsider.
        – Gerry Myerson
        Aug 3 at 2:42














      up vote
      4
      down vote













      Hint: recall that $5^x+3=5^x cdot 5^3$. Can you take it from here?






      share|cite|improve this answer





















      • Hello, thanks for the speedy response. I see how to factor 5^x from 5^x+3 however i don't understand how to obtain the answer 5^x x 126. I have 5^x + (5^x x 125). how can i simplify further from this stage?
        – Sam Kha
        Aug 2 at 13:42






      • 1




        @SamKha Use the fact that $a + bcdot a = (1+b)cdot a$
        – 5xum
        Aug 2 at 13:47






      • 1




        Sorry to see you withdraw from the moderator election, Zachary. I hope you'll reconsider.
        – Gerry Myerson
        Aug 3 at 2:42












      up vote
      4
      down vote










      up vote
      4
      down vote









      Hint: recall that $5^x+3=5^x cdot 5^3$. Can you take it from here?






      share|cite|improve this answer













      Hint: recall that $5^x+3=5^x cdot 5^3$. Can you take it from here?







      share|cite|improve this answer













      share|cite|improve this answer



      share|cite|improve this answer











      answered Aug 2 at 13:31







      user223391


















      • Hello, thanks for the speedy response. I see how to factor 5^x from 5^x+3 however i don't understand how to obtain the answer 5^x x 126. I have 5^x + (5^x x 125). how can i simplify further from this stage?
        – Sam Kha
        Aug 2 at 13:42






      • 1




        @SamKha Use the fact that $a + bcdot a = (1+b)cdot a$
        – 5xum
        Aug 2 at 13:47






      • 1




        Sorry to see you withdraw from the moderator election, Zachary. I hope you'll reconsider.
        – Gerry Myerson
        Aug 3 at 2:42
















      • Hello, thanks for the speedy response. I see how to factor 5^x from 5^x+3 however i don't understand how to obtain the answer 5^x x 126. I have 5^x + (5^x x 125). how can i simplify further from this stage?
        – Sam Kha
        Aug 2 at 13:42






      • 1




        @SamKha Use the fact that $a + bcdot a = (1+b)cdot a$
        – 5xum
        Aug 2 at 13:47






      • 1




        Sorry to see you withdraw from the moderator election, Zachary. I hope you'll reconsider.
        – Gerry Myerson
        Aug 3 at 2:42















      Hello, thanks for the speedy response. I see how to factor 5^x from 5^x+3 however i don't understand how to obtain the answer 5^x x 126. I have 5^x + (5^x x 125). how can i simplify further from this stage?
      – Sam Kha
      Aug 2 at 13:42




      Hello, thanks for the speedy response. I see how to factor 5^x from 5^x+3 however i don't understand how to obtain the answer 5^x x 126. I have 5^x + (5^x x 125). how can i simplify further from this stage?
      – Sam Kha
      Aug 2 at 13:42




      1




      1




      @SamKha Use the fact that $a + bcdot a = (1+b)cdot a$
      – 5xum
      Aug 2 at 13:47




      @SamKha Use the fact that $a + bcdot a = (1+b)cdot a$
      – 5xum
      Aug 2 at 13:47




      1




      1




      Sorry to see you withdraw from the moderator election, Zachary. I hope you'll reconsider.
      – Gerry Myerson
      Aug 3 at 2:42




      Sorry to see you withdraw from the moderator election, Zachary. I hope you'll reconsider.
      – Gerry Myerson
      Aug 3 at 2:42










      up vote
      1
      down vote













      We have



      $$5^x+5^x+3=5^x+5^xcdot 5^3=5^x(1+125)=126cdot 5^x$$






      share|cite|improve this answer

























        up vote
        1
        down vote













        We have



        $$5^x+5^x+3=5^x+5^xcdot 5^3=5^x(1+125)=126cdot 5^x$$






        share|cite|improve this answer























          up vote
          1
          down vote










          up vote
          1
          down vote









          We have



          $$5^x+5^x+3=5^x+5^xcdot 5^3=5^x(1+125)=126cdot 5^x$$






          share|cite|improve this answer













          We have



          $$5^x+5^x+3=5^x+5^xcdot 5^3=5^x(1+125)=126cdot 5^x$$







          share|cite|improve this answer













          share|cite|improve this answer



          share|cite|improve this answer











          answered Aug 2 at 13:49









          gimusi

          63.8k73480




          63.8k73480




















              up vote
              0
              down vote













              Using index laws,
              $$5^x + 3 = 5^x cdot 5^3 = 125 cdot 5^x.$$



              Note that this is different from the situation $5^x + 5^3$, where $5^x$ would indeed have to be a factor of $5^3$ in order to (cleanly) take it out as a divisor.






              share|cite|improve this answer

























                up vote
                0
                down vote













                Using index laws,
                $$5^x + 3 = 5^x cdot 5^3 = 125 cdot 5^x.$$



                Note that this is different from the situation $5^x + 5^3$, where $5^x$ would indeed have to be a factor of $5^3$ in order to (cleanly) take it out as a divisor.






                share|cite|improve this answer























                  up vote
                  0
                  down vote










                  up vote
                  0
                  down vote









                  Using index laws,
                  $$5^x + 3 = 5^x cdot 5^3 = 125 cdot 5^x.$$



                  Note that this is different from the situation $5^x + 5^3$, where $5^x$ would indeed have to be a factor of $5^3$ in order to (cleanly) take it out as a divisor.






                  share|cite|improve this answer













                  Using index laws,
                  $$5^x + 3 = 5^x cdot 5^3 = 125 cdot 5^x.$$



                  Note that this is different from the situation $5^x + 5^3$, where $5^x$ would indeed have to be a factor of $5^3$ in order to (cleanly) take it out as a divisor.







                  share|cite|improve this answer













                  share|cite|improve this answer



                  share|cite|improve this answer











                  answered Aug 2 at 13:32









                  Theo Bendit

                  11.7k1841




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