- #1
Emperor
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Homework Statement
If f(x) = mx^3 + gx^2 - x + 3 is divided by x - 1, the remainder is 3. If f(x) is divided by x + 3, the remainder is -1. What are the values of m and g?
Homework Equations
Remainder Theorum/Factor Theorum
The Attempt at a Solution
Here is what I did:
f(x)=mx^3+gx^2-x+3
x -1 remainder = 3
3=m(1)^3+g(1)^2-(1)+3
3=m+g-1+3
1=m+g
x + 3, remainder = -1
-7=m(-3)^3+g(-3)^2-(-3)+3
-7=-27m+9g+3+3
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Past that point is where I start getting fractions to my answers which don't lead me anywhere close to my answer. Where did I make a mistake and how can I solve it?