SOLUTION: Find q(x) such that 3x^3 - 5x^2 - x + 4 = (3x + 1)q(x) + (10x + 7)

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Question 1113140: Find q(x) such that 3x^3 - 5x^2 - x + 4 = (3x + 1)q(x) + (10x + 7)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let q%28x%29=ax%5E2%2Bbx%2Bc,
So,
+%283x+%2B+1%29%28ax%5E2%2Bbx%2Bc%29+%2B+%2810x+%2B+7%29=3x%5E3+-+5x%5E2+-+x+%2B+4

+3ax%5E3%2B%283b%2Ba%29x%5E2%2B%283c%2B10%29x%2B%28c%2B+7%29=3x%5E3+-+5x%5E2+-+x+%2B+4
So term by term,
3ax%5E3=3x%5E3
3a=3
a=1
Next,
%283b%2Ba%29x%5E2=-5x%5E2
3b%2B1=-5
3b=-6
b=-2
Continue on to solve for c similarly.