How do you find the factor of a polynomial with the remainders of polynomials that are being divided?
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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
edited 2 hours ago
jmerry
1,961210
asked 2 hours ago
CosmoCrash
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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
edited 2 hours ago
jmerry
1,961210
asked 2 hours ago
CosmoCrash
13
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.
add a comment |
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
edited 2 hours ago
jmerry
1,961210
asked 2 hours ago
CosmoCrash
13
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
edited 2 hours ago
jmerry
1,961210
asked 2 hours ago
CosmoCrash
13
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.
edited 2 hours ago
jmerry
1,961210
asked 2 hours ago
CosmoCrash
13
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.
edited 2 hours ago
jmerry
1,961210
edited 2 hours ago
jmerry
1,961210
edited 2 hours ago
jmerry
1,961210
1,961210
asked 2 hours ago
CosmoCrash
13
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.
asked 2 hours ago
CosmoCrash
13
asked 2 hours ago
CosmoCrash
13
13
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.
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.
add a comment |
add a comment |
1 Answer
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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 $x+2$?
answered 2 hours ago
jmerry
1,961210
I solved the problem and got a = 0 , b = 2 but it says that's wrong
– CosmoCrash
1 hour ago
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
1 hour ago
add a comment |
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1 Answer
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1 Answer
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oldest
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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 $x+2$?
answered 2 hours ago
jmerry
1,961210
I solved the problem and got a = 0 , b = 2 but it says that's wrong
– CosmoCrash
1 hour ago
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
1 hour ago
add a comment |
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 $x+2$?
answered 2 hours ago
jmerry
1,961210
I solved the problem and got a = 0 , b = 2 but it says that's wrong
– CosmoCrash
1 hour ago
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
1 hour ago
add a comment |
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 $x+2$?
answered 2 hours ago
jmerry
1,961210
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 $x+2$?
answered 2 hours ago
jmerry
1,961210
answered 2 hours ago
jmerry
1,961210
answered 2 hours ago
jmerry
1,961210
answered 2 hours ago
jmerry
1,961210
1,961210
I solved the problem and got a = 0 , b = 2 but it says that's wrong
– CosmoCrash
1 hour ago
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
1 hour ago
add a comment |
I solved the problem and got a = 0 , b = 2 but it says that's wrong
– CosmoCrash
1 hour ago
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
1 hour ago
I solved the problem and got a = 0 , b = 2 but it says that's wrong
– CosmoCrash
1 hour ago
I solved the problem and got a = 0 , b = 2 but it says that's wrong
– CosmoCrash
1 hour ago
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
1 hour ago
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
1 hour ago
add a comment |
CosmoCrash is a new contributor. Be nice, and check out our Code of Conduct.
CosmoCrash is a new contributor. Be nice, and check out our Code of Conduct.
CosmoCrash is a new contributor. Be nice, and check out our Code of Conduct.
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