Find a polynomial \( q(x)\) such that \((x+1)^3+x^2\cdot q(x)\) has degree less than \(2\).
Here is how:
\((x+1)^3+x^2\cdot q(x)\\ =x^3+3x^2+3x+1+x^2\cdot q(x)\\ =x^2(x+3)+3x+1+x^2\cdot q(x)\\ =x^2(x+3+q(x))+3x+1\\ if\;\;q(x)=-3-x\\ \text{Then the degree of the resuling polynomial will be 1} \)
Thanks a lot!
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