$$f(x)=ax^3+bx^2+3x+4$$ $f(x)$ 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?
2026-04-24 05:15:52.1777007752
Cubic polynomial given linear reminders after division by quadratic polynomials
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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?