<PRE><B>Question 190675</B>
a)If (x-2) is a factor of 2x^3 + 3x + k, find k.
Using synthetic division:
2)....2....0....3....k
.......2....4....11..|..k+22

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Remainder is k+22 = 0 , since x-2 is a factor.
Therefore k = -22
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b)When ax^3 + 4x^2 + 5x - 3 is divided by (x-2) and (x-1), the remainders are equal. Find a
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2)....a....4........5.......-3
.......a....4+2a....4a+13...|..8a+23

1st remainder is 8a+23
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1)....a....4........5.......-3
.......a....4+a.....a+9....|..a+6
 
2nd remainder is a+6
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Equation:
8a+23 = a+6
7a = -17
a = -17/7
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Cheers,
Stan H.</PRE>