Find p and q of this polynomial division [duplicate]
This question already has an answer here:
$ax^3+8x^2+bx+6$ is exactly divisible by $x^2-2x-3$, find the values of $a$ and $b$
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Dividing $x^4 + px^3 + qx^2 - 16x -12 \$ by $(x+1)(x+3)$, the remainder is $2x+3$, find $p$ and $q$
I dont know how to solve this, please i need help
regards.
algebra-precalculus polynomials
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2 days ago
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This question already has an answer here:
$ax^3+8x^2+bx+6$ is exactly divisible by $x^2-2x-3$, find the values of $a$ and $b$
9 answers
Dividing $x^4 + px^3 + qx^2 - 16x -12 \$ by $(x+1)(x+3)$, the remainder is $2x+3$, find $p$ and $q$
I dont know how to solve this, please i need help
regards.
algebra-precalculus polynomials
edited 2 days ago
José Carlos Santos
152k22123226
asked 2 days ago
englishworkvgsenglishworkvgs
62
marked as duplicate by Bill Dubuque algebra-precalculus
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2 days ago
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
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This question already has an answer here:
$ax^3+8x^2+bx+6$ is exactly divisible by $x^2-2x-3$, find the values of $a$ and $b$
9 answers
Dividing $x^4 + px^3 + qx^2 - 16x -12 \$ by $(x+1)(x+3)$, the remainder is $2x+3$, find $p$ and $q$
I dont know how to solve this, please i need help
regards.
algebra-precalculus polynomials
edited 2 days ago
José Carlos Santos
152k22123226
asked 2 days ago
englishworkvgsenglishworkvgs
62
This question already has an answer here:
$ax^3+8x^2+bx+6$ is exactly divisible by $x^2-2x-3$, find the values of $a$ and $b$
9 answers
Dividing $x^4 + px^3 + qx^2 - 16x -12 \$ by $(x+1)(x+3)$, the remainder is $2x+3$, find $p$ and $q$
I dont know how to solve this, please i need help
regards.
This question already has an answer here:
$ax^3+8x^2+bx+6$ is exactly divisible by $x^2-2x-3$, find the values of $a$ and $b$
9 answers
algebra-precalculus polynomials
algebra-precalculus polynomials
edited 2 days ago
José Carlos Santos
152k22123226
asked 2 days ago
englishworkvgsenglishworkvgs
62
edited 2 days ago
José Carlos Santos
152k22123226
asked 2 days ago
englishworkvgsenglishworkvgs
62
edited 2 days ago
José Carlos Santos
152k22123226
edited 2 days ago
José Carlos Santos
152k22123226
edited 2 days ago
José Carlos Santos
152k22123226
152k22123226
asked 2 days ago
englishworkvgsenglishworkvgs
62
asked 2 days ago
englishworkvgsenglishworkvgs
62
asked 2 days ago
englishworkvgsenglishworkvgs
62
62
marked as duplicate by Bill Dubuque algebra-precalculus
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2 days ago
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You know that, for some quadratic polynomial $P(x)$, you have$$x^4+px^3+qx^2-16x-12=(x+1)(x+3)P(x)+2x+3.$$Which information do you extract from this if you put $x=-1$? And what if you put $x=-3$?
answered 2 days ago
José Carlos SantosJosé Carlos Santos
152k22123226
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First substruct $2x+3$ from $p(x)=x^4 + px^3 + qx^2 - 16x -12 \$
begin{align}
q(x) &= p(x) - (2x+3) \
&= x^4 + px^3 + qx^2 - 16x -12 - 2x -3\
&= x^4 + px^3 + qx^2 -18x -15
end{align}
Now, $(x+1)|q(x)$ and $(x+3)|q(x)$
Calculate $q(-1)=0$ and $q(-3)$ to solve $p$ and $q$
answered 2 days ago
kelalakakelalaka
242212
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2 Answers
2
active
oldest
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2 Answers
2
active
oldest
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active
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active
oldest
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You know that, for some quadratic polynomial $P(x)$, you have$$x^4+px^3+qx^2-16x-12=(x+1)(x+3)P(x)+2x+3.$$Which information do you extract from this if you put $x=-1$? And what if you put $x=-3$?
answered 2 days ago
José Carlos SantosJosé Carlos Santos
152k22123226
add a comment |
You know that, for some quadratic polynomial $P(x)$, you have$$x^4+px^3+qx^2-16x-12=(x+1)(x+3)P(x)+2x+3.$$Which information do you extract from this if you put $x=-1$? And what if you put $x=-3$?
answered 2 days ago
José Carlos SantosJosé Carlos Santos
152k22123226
add a comment |
You know that, for some quadratic polynomial $P(x)$, you have$$x^4+px^3+qx^2-16x-12=(x+1)(x+3)P(x)+2x+3.$$Which information do you extract from this if you put $x=-1$? And what if you put $x=-3$?
answered 2 days ago
José Carlos SantosJosé Carlos Santos
152k22123226
You know that, for some quadratic polynomial $P(x)$, you have$$x^4+px^3+qx^2-16x-12=(x+1)(x+3)P(x)+2x+3.$$Which information do you extract from this if you put $x=-1$? And what if you put $x=-3$?
answered 2 days ago
José Carlos SantosJosé Carlos Santos
152k22123226
edited 2 days ago
answered 2 days ago
José Carlos SantosJosé Carlos Santos
152k22123226
answered 2 days ago
José Carlos SantosJosé Carlos Santos
152k22123226
answered 2 days ago
José Carlos SantosJosé Carlos Santos
152k22123226
152k22123226
add a comment |
add a comment |
First substruct $2x+3$ from $p(x)=x^4 + px^3 + qx^2 - 16x -12 \$
begin{align}
q(x) &= p(x) - (2x+3) \
&= x^4 + px^3 + qx^2 - 16x -12 - 2x -3\
&= x^4 + px^3 + qx^2 -18x -15
end{align}
Now, $(x+1)|q(x)$ and $(x+3)|q(x)$
Calculate $q(-1)=0$ and $q(-3)$ to solve $p$ and $q$
answered 2 days ago
kelalakakelalaka
242212
add a comment |
First substruct $2x+3$ from $p(x)=x^4 + px^3 + qx^2 - 16x -12 \$
begin{align}
q(x) &= p(x) - (2x+3) \
&= x^4 + px^3 + qx^2 - 16x -12 - 2x -3\
&= x^4 + px^3 + qx^2 -18x -15
end{align}
Now, $(x+1)|q(x)$ and $(x+3)|q(x)$
Calculate $q(-1)=0$ and $q(-3)$ to solve $p$ and $q$
answered 2 days ago
kelalakakelalaka
242212
add a comment |
First substruct $2x+3$ from $p(x)=x^4 + px^3 + qx^2 - 16x -12 \$
begin{align}
q(x) &= p(x) - (2x+3) \
&= x^4 + px^3 + qx^2 - 16x -12 - 2x -3\
&= x^4 + px^3 + qx^2 -18x -15
end{align}
Now, $(x+1)|q(x)$ and $(x+3)|q(x)$
Calculate $q(-1)=0$ and $q(-3)$ to solve $p$ and $q$
answered 2 days ago
kelalakakelalaka
242212
First substruct $2x+3$ from $p(x)=x^4 + px^3 + qx^2 - 16x -12 \$
begin{align}
q(x) &= p(x) - (2x+3) \
&= x^4 + px^3 + qx^2 - 16x -12 - 2x -3\
&= x^4 + px^3 + qx^2 -18x -15
end{align}
Now, $(x+1)|q(x)$ and $(x+3)|q(x)$
Calculate $q(-1)=0$ and $q(-3)$ to solve $p$ and $q$
answered 2 days ago
kelalakakelalaka
242212
answered 2 days ago
kelalakakelalaka
242212
answered 2 days ago
kelalakakelalaka
242212
answered 2 days ago
kelalakakelalaka
242212
242212
add a comment |
add a comment |
