Standard +0.3 This is a straightforward polynomial division problem requiring students to equate coefficients after multiplying out (divisor × quotient + remainder = dividend). While it involves algebraic manipulation across multiple terms, it's a standard C4 exercise with a clear method and no conceptual surprises—slightly easier than average.
3 When \(x ^ { 4 } - 2 x ^ { 3 } - 7 x ^ { 2 } + 7 x + a\) is divided by \(x ^ { 2 } + 2 x - 1\), the quotient is \(x ^ { 2 } + b x + 2\) and the remainder is \(c x + 7\). Find the values of the constants \(a , b\) and \(c\).
3 When $x ^ { 4 } - 2 x ^ { 3 } - 7 x ^ { 2 } + 7 x + a$ is divided by $x ^ { 2 } + 2 x - 1$, the quotient is $x ^ { 2 } + b x + 2$ and the remainder is $c x + 7$. Find the values of the constants $a , b$ and $c$.
\hfill \mbox{\textit{OCR C4 2008 Q3 [5]}}