Đáp án:
\(Q\left( x \right) = {x^2} + 5x + 13\)
Giải thích các bước giải:
\(\begin{array}{l}
Q(x).(x - 2) + 28 = ({x^2} + x + 1).(x + 2)\\
\to Q(x).(x - 2) + 28 = {x^3} + {x^2} + x + 2{x^2} + 2x + 2\\
\to Q(x).(x - 2) = {x^3} + 3{x^2} + 3x - 26\\
\to Q\left( x \right) = \dfrac{{{x^3} + 3{x^2} + 3x - 26}}{{x - 2}} = \dfrac{{{x^3} - 2{x^2} + 5{x^2} - 10x + 13x - 26}}{{x - 2}}\\
= \dfrac{{{x^2}\left( {x - 2} \right) + 5x\left( {x - 2} \right) + 13\left( {x - 2} \right)}}{{x - 2}}\\
= \dfrac{{\left( {x - 2} \right)\left( {{x^2} + 5x + 13} \right)}}{{x - 2}} = {x^2} + 5x + 13
\end{array}\)
