SOLUTION: Use synthetic division to find the quotient and the remainder. (3x^4-2x^2+2)/(x-1/4)

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Question 1129057: Use synthetic division to find the quotient and the remainder.
(3x^4-2x^2+2)/(x-1/4)
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Use synthetic division to find the quotient and the remainder.
(3x^4-2x^2+2)/(x-1/4)
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(1/4)...3....0.......-2........0..........2
........3...3/4...-29/16.....-29/64...|-29/256+(512/256) = 483/256
Quotient:: 3x^3 + (3/4)x^2 - (29/16)x -29/64
Remainder:: 483/256
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Cheers,
Stan H.
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Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%5E4-2x%5E2%2B2%29%2F%28x-1%2F4%29+


write down the coefficients of the polynomial and put the zero from x-1%2F4=0 ( x=1%2F4 ) at the left

1%2F4|| 3 −−−−−− +0+−−−−−− -2 −−−−−− +0 −−−−−− +2

bring down the leading coefficient to the bottom row.

1%2F4|| 3 −−−−−− +0+−−−−−− -2 −−−−−− +0 −−−−−− +2
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
−−−−3

multiply by the number on the left, and carry the result into the next column: %281%2F4%293=3%2F4

1%2F4|| 3 −−−−−− +0+−−−−−− +-2 −−−−−− +0+ −−−−−− 2
−−−−−−−−−−−−3%2F4−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
−−−−3

add down the column: 0%2B3%2F4=3%2F4
1%2F4|| 3 −−−−−− 0 −−−−−− -2+−−−−−− +0 −−−−−− 2
−−−−−−−−−−−−3%2F4−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
−−−−3−−−−−−−3%2F4

multiply by the number on the left, and carry the result into the next column: %281%2F4%29%283%2F4%29=3%2F16

1%2F4|| 3 −−−−−− +0 −−−−−− ++-2 −−−−−− +++0 −−−−−− +2
−−−−−−−−−−−−3%2F4−−−−−−−−−−3%2F16−−−−−−−−−−−−−−−−−−−−−−−−
−−−−3−−−−−−−3%2F4


add down the column: -2%2B3%2F16=-29%2F16

1%2F4|| 3 −−−−−− +0 −−−−−− ++-2 −−−−−− ++0+ −−−−−− +2
−−−−−−−−−−−−3%2F4−−−−−−−−−−3%2F16−−−−−−−−−−−−−−−−−−−−−−−−
−−−−3−−−−−−−3%2F4−−−−−−−−−..-29%2F16


multiply by the number on the left, and carry the result into the next column:+%281%2F4%29%28-29%2F16%29=-29%2F64

1%2F4|| 3 −−−−−− +0 −−−−−− +-2 −−−−−− ++0 −−−−−− 2
−−−−−−−−−−−−3%2F4−−−−−−−−−−3%2F16−−−−−..-29%2F64−−−−−−−−−−−−−−−−−
−−−−3−−−−−−−3%2F4−−−−−−−−−..-29%2F16
add down the column: 0%2B%28-29%2F64%29=-29%2F64

1%2F4|| 3 −−−−−− +0 −−−−−− +-2 −−−−−− +0 −−−−−− 2
−−−−−−−−−−−−3%2F4−−−−−−−−−−3%2F16−−−−−..-29%2F64−−−−−−−−−−−−−−−−−
−−−−3−−−−−−−3%2F4−−−−−−−−−..-29%2F16−−−..-29%2F64

multiply by the number on the left, and carry the result into the next column: %281%2F4%29%28-29%2F64%29=-29%2F256

1%2F4|| 3 −−−−−− +0 −−−−−− ++-2 −−−−−− +0 −−−−−− 2
−−−−−−−−−−−−3%2F4−−−−−−−−−−3%2F16−−−−−..-29%2F64−−−−−29%2F256−−−−−−−−−−−
−−−−3−−−−−−−3%2F4−−−−−−−−−..-29%2F16−−−..-29%2F64

add down the column:+2%2B%28-29%2F256%29=483%2F256

1%2F4|| 3 −−−−−− +0 −−−−−− ++-2 −−−−−− +0+ −−−−−− 2
−−−−−−−−−−−−3%2F4−−−−−−−−−−3%2F16−−−−−..-29%2F64−−−−−29%2F256−−−−−−−−−−−
−−−−3−−−−−−−3%2F4−−−−−−−−−..-29%2F16−−−..-29%2F64−−−−−483%2F256