Moderate -0.8 This is a straightforward application of the factor theorem requiring students to verify f(2)=0, then perform polynomial division to find the quadratic factor, and finally solve by factoring or using the quadratic formula. It's a standard C1 textbook exercise with clear steps and no novel insight required, making it easier than average.
7 Show that ( \(x - 2\) ) is a factor of \(\mathrm { f } ( x ) = x ^ { 3 } - x ^ { 2 } - 4 x + 4\).
Hence solve the equation \(x ^ { 3 } - x ^ { 2 } - 4 x + 4 = 0\).
7 Show that ( $x - 2$ ) is a factor of $\mathrm { f } ( x ) = x ^ { 3 } - x ^ { 2 } - 4 x + 4$.\\
Hence solve the equation $x ^ { 3 } - x ^ { 2 } - 4 x + 4 = 0$.
\hfill \mbox{\textit{OCR MEI C1 Q7 [5]}}