SOLUTION: When x^3+cx+d is divided by x+1, the remainder is 3, and when it is divided by x-2, the remainder is -3. Determine the values of c and d.
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Question 177074: When x^3+cx+d is divided by x+1, the remainder is 3, and when it is divided by x-2, the remainder is -3. Determine the values of c and d.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
When x^3+cx+d is divided by x+1, the remainder is 3
So f(-1) = -1 -c + d = 3
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and when it is divided by x-2, the remainder is -3
So f(2) = 8 + 2c + d = -3
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Determine the values of c and d.
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Rearrange to get:
-c + d = 3
2c + d = -11
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Simplify:
-2c + 2d = 6
2c + d = -11
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Add to solve for "d":
3d = -5
d = -5/3
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Substitute to solve for "c":
c = d -3
c = (-5/3) - 3
c = (-5/3) - (9/3) = -14/3
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Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You need to use polynomial long division to divide by . Remember to include the missing term, so your dividend becomes . Rendering polynomial long division on this site is very difficult, so I'm just going to hope you know how to do that. You will find that the remainder is which you are told is equal to 3.
Do the polynomial long division again, this time using as a divisor and you will discover that the remainder is which you are told is equal to -3.
Now you have two 2-variable linear equations:
=> and
=>
Solve this system for c and d to get your answer.
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