Question 10: Calculate \( x\left( {{x^2} + x + 1} \right) – {x^2}\left( {x + 1} \right) – x + 5\)

We have:

\(\begin{array}{l} x\left( {{x^2} + x + 1} \right) – {x^2}\left( {x + 1} \right) – x + 5\ \ = x. {x^2} + xx + x.1 – {x^2}.x – x.1 – x + 5\\ = {x^3} + {x^2} + x – {x ^3} – {x^2} – x + 5\\ = ({x^3} – {x^3}) + ({x^2} – {x^2}) + (x – x) + 5 = 5 \end{array}\)