Question 1049745
The polynomial f(x) is given by f(x) =4x^3 +ax^2 + bx+2. (4x+1) is a factor of f(x).When f(x) is divided by (x-1) there is a remainder of 20. Find a and b. 
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Using synthetic division::
(-1/4)....4....a..........b..............2
.........4...a-1..-(1/4)a+(1/4)+b....|(1/16)a-(1/16)-(1/4)b+b

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1st equation:: (1/16)a - (1/16) + (3/4)b = 0

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1)....4.....a......b......2
......4....a+4...a+b+4...|.. a + b + 6
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2nd equation:: a+b+6 = 20
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Solve 2nd eq for "a" and substitute in 1st to solve for "b"::
a = 14-b
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(1/16)(14-b) - (1/16) + (12/16)b = 0
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14-b - 1 + 12b = 0
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11b = -13
b = -13/11
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a = 14-b = 14+13/11 = 167/11
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Cheers,
Stan H.
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