How do you find the factor of a polynomial with the remainders of polynomials that are being divided? [on...












0














I don't understand how to do this problem. I need to determine constants a and b based of the remainders of two polynomials divided by f(x)




When a polynomial expression $f(x)$ is divided by $x^2-4$ the remainder is $ax+b$. Determine the constants $a$ and $b$, given that $x-2$ is a factor of $f(x)$ and also that when $f(x)$ is divided by $x+2$, the remainder is $8$.







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put on hold as off-topic by Nosrati, Paul Frost, Pierre-Guy Plamondon, mrtaurho, amWhy Jan 4 at 14:13


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Nosrati, Paul Frost, Pierre-Guy Plamondon, mrtaurho, amWhy

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  • See this answer for an easy way
    – Bill Dubuque
    Jan 4 at 19:32
















0














I don't understand how to do this problem. I need to determine constants a and b based of the remainders of two polynomials divided by f(x)




When a polynomial expression $f(x)$ is divided by $x^2-4$ the remainder is $ax+b$. Determine the constants $a$ and $b$, given that $x-2$ is a factor of $f(x)$ and also that when $f(x)$ is divided by $x+2$, the remainder is $8$.







polynomials







share|cite|improve this question









New contributor




CosmoCrash is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











put on hold as off-topic by Nosrati, Paul Frost, Pierre-Guy Plamondon, mrtaurho, amWhy Jan 4 at 14:13


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Nosrati, Paul Frost, Pierre-Guy Plamondon, mrtaurho, amWhy

If this question can be reworded to fit the rules in the help center, please edit the question.













  • See this answer for an easy way
    – Bill Dubuque
    Jan 4 at 19:32














0












0








0







I don't understand how to do this problem. I need to determine constants a and b based of the remainders of two polynomials divided by f(x)




When a polynomial expression $f(x)$ is divided by $x^2-4$ the remainder is $ax+b$. Determine the constants $a$ and $b$, given that $x-2$ is a factor of $f(x)$ and also that when $f(x)$ is divided by $x+2$, the remainder is $8$.







polynomials







share|cite|improve this question









New contributor




CosmoCrash is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











I don't understand how to do this problem. I need to determine constants a and b based of the remainders of two polynomials divided by f(x)




When a polynomial expression $f(x)$ is divided by $x^2-4$ the remainder is $ax+b$. Determine the constants $a$ and $b$, given that $x-2$ is a factor of $f(x)$ and also that when $f(x)$ is divided by $x+2$, the remainder is $8$.







polynomials




polynomials






share|cite|improve this question









New contributor




CosmoCrash is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




CosmoCrash is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question








edited Jan 4 at 7:07









jmerry

2,521312




2,521312






New contributor




CosmoCrash is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked Jan 4 at 7:00









CosmoCrashCosmoCrash

13




13




New contributor




CosmoCrash is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor





CosmoCrash is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






CosmoCrash is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




put on hold as off-topic by Nosrati, Paul Frost, Pierre-Guy Plamondon, mrtaurho, amWhy Jan 4 at 14:13


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Nosrati, Paul Frost, Pierre-Guy Plamondon, mrtaurho, amWhy

If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by Nosrati, Paul Frost, Pierre-Guy Plamondon, mrtaurho, amWhy Jan 4 at 14:13


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Nosrati, Paul Frost, Pierre-Guy Plamondon, mrtaurho, amWhy

If this question can be reworded to fit the rules in the help center, please edit the question.












  • See this answer for an easy way
    – Bill Dubuque
    Jan 4 at 19:32


















  • See this answer for an easy way
    – Bill Dubuque
    Jan 4 at 19:32
















See this answer for an easy way
– Bill Dubuque
Jan 4 at 19:32




See this answer for an easy way
– Bill Dubuque
Jan 4 at 19:32










1 Answer
1






active

oldest

votes


















0














The key to this problem is that $x-2$ and $x-4$ are the factors of $x^2-4$.



Suppose we split $f$ into two parts through that division: $f(x) = (x^2-4)g(x) + ax+b$. What does it look like if we divide that by $x-2$? By $x+2$?






share|cite|improve this answer





















  • I solved the problem and got a = 0 , b = 2 but it says that's wrong
    – CosmoCrash
    Jan 4 at 7:24










  • Indeed. That would be a remainder of $2$ when divided by $x-2$ and a remainder of $2$ when divided by $x+2$. We can't say more unless you say more about what you've tried to do.
    – jmerry
    Jan 4 at 8:00


















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









0














The key to this problem is that $x-2$ and $x-4$ are the factors of $x^2-4$.



Suppose we split $f$ into two parts through that division: $f(x) = (x^2-4)g(x) + ax+b$. What does it look like if we divide that by $x-2$? By $x+2$?






share|cite|improve this answer





















  • I solved the problem and got a = 0 , b = 2 but it says that's wrong
    – CosmoCrash
    Jan 4 at 7:24










  • Indeed. That would be a remainder of $2$ when divided by $x-2$ and a remainder of $2$ when divided by $x+2$. We can't say more unless you say more about what you've tried to do.
    – jmerry
    Jan 4 at 8:00
















0














The key to this problem is that $x-2$ and $x-4$ are the factors of $x^2-4$.



Suppose we split $f$ into two parts through that division: $f(x) = (x^2-4)g(x) + ax+b$. What does it look like if we divide that by $x-2$? By $x+2$?






share|cite|improve this answer





















  • I solved the problem and got a = 0 , b = 2 but it says that's wrong
    – CosmoCrash
    Jan 4 at 7:24










  • Indeed. That would be a remainder of $2$ when divided by $x-2$ and a remainder of $2$ when divided by $x+2$. We can't say more unless you say more about what you've tried to do.
    – jmerry
    Jan 4 at 8:00














0












0








0






The key to this problem is that $x-2$ and $x-4$ are the factors of $x^2-4$.



Suppose we split $f$ into two parts through that division: $f(x) = (x^2-4)g(x) + ax+b$. What does it look like if we divide that by $x-2$? By $x+2$?






share|cite|improve this answer












The key to this problem is that $x-2$ and $x-4$ are the factors of $x^2-4$.



Suppose we split $f$ into two parts through that division: $f(x) = (x^2-4)g(x) + ax+b$. What does it look like if we divide that by $x-2$? By $x+2$?







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Jan 4 at 7:10









jmerryjmerry

2,521312




2,521312












  • I solved the problem and got a = 0 , b = 2 but it says that's wrong
    – CosmoCrash
    Jan 4 at 7:24










  • Indeed. That would be a remainder of $2$ when divided by $x-2$ and a remainder of $2$ when divided by $x+2$. We can't say more unless you say more about what you've tried to do.
    – jmerry
    Jan 4 at 8:00


















  • I solved the problem and got a = 0 , b = 2 but it says that's wrong
    – CosmoCrash
    Jan 4 at 7:24










  • Indeed. That would be a remainder of $2$ when divided by $x-2$ and a remainder of $2$ when divided by $x+2$. We can't say more unless you say more about what you've tried to do.
    – jmerry
    Jan 4 at 8:00
















I solved the problem and got a = 0 , b = 2 but it says that's wrong
– CosmoCrash
Jan 4 at 7:24




I solved the problem and got a = 0 , b = 2 but it says that's wrong
– CosmoCrash
Jan 4 at 7:24












Indeed. That would be a remainder of $2$ when divided by $x-2$ and a remainder of $2$ when divided by $x+2$. We can't say more unless you say more about what you've tried to do.
– jmerry
Jan 4 at 8:00




Indeed. That would be a remainder of $2$ when divided by $x-2$ and a remainder of $2$ when divided by $x+2$. We can't say more unless you say more about what you've tried to do.
– jmerry
Jan 4 at 8:00



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