$$f(x)=ax^3+bx^2+3x+4$$ $f(x)$ leaves a remainder of $-3x+3$ when divided by $x^2-1$. What would you suggest to solve for a and b solely using the remainder, factor and the integral zero theorems?
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Adapt any of the answers under the closely related question here. – dxiv Jan 31 '22 at 06:33
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$f(1) = -3\cdot 1+3 = 0\implies a+b+7 = 0$. Also $f(-1) = -3\cdot (-1)+3 = 6 \implies -a+b+1=6 $. Can you take it from here?
Wang YeFei
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