SOLUTION: Could someone please help me with the following question. Please!!! a)If (x-2) is a factor of 2x^3 + 3x + k, find k.(3 marks) b)When ax^3 + 4x^2 + 5x

SOLUTION: Could someone please help me with the following question. Please!!! a)If (x-2) is a factor of 2x^3 + 3x + k, find k.(3 marks) b)When ax^3 + 4x^2 + 5x - 3 is divided by (x-2) an

Question 190675: Could someone please help me with the following question. Please!!!
a)If (x-2) is a factor of 2x^3 + 3x + k, find k.(3 marks)
b)When ax^3 + 4x^2 + 5x - 3 is divided by (x-2) and (x-1), the remainders are equal. Find a.(4 marks)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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
----------------
Remainder is k+22 = 0 , since x-2 is a factor.
Therefore k = -22
==========================
b)When ax^3 + 4x^2 + 5x - 3 is divided by (x-2) and (x-1), the remainders are equal. Find a
----------------
2)....a....4........5.......-3
.......a....4+2a....4a+13...|..8a+23
1st remainder is 8a+23
=========================================
1)....a....4........5.......-3
.......a....4+a.....a+9....|..a+6

2nd remainder is a+6
=========================================
Equation:
8a+23 = a+6
7a = -17
a = -17/7
===========================================
Cheers,
Stan H.
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