Moderate -0.8 This is a straightforward application of the factor theorem requiring substitution of x = -1/2 to verify the factor, followed by polynomial division and factorising a quadratic. All steps are routine A-level techniques with no problem-solving insight needed, making it easier than average but not trivial due to the arithmetic involved with fractions and the 5-mark allocation.
5.
\(\mathrm { p } ( x ) = 30 x ^ { 3 } - 7 x ^ { 2 } - 7 x + 2\)
Prove that ( \(2 x + 1\) ) is a factor of \(\mathrm { p } ( x )\)
[0pt]
[2 marks]
L
L
L
L
L
L
Factorise \(\mathrm { p } ( x )\) completely. [0pt]
[3 marks]
L
L
L
L
L
5.\\
$\mathrm { p } ( x ) = 30 x ^ { 3 } - 7 x ^ { 2 } - 7 x + 2$\\
Prove that ( $2 x + 1$ ) is a factor of $\mathrm { p } ( x )$\\[0pt]
[2 marks]\\
L\\
L\\
L\\
L\\
L\\
L
Factorise $\mathrm { p } ( x )$ completely.\\[0pt]
[3 marks]\\
L\\
L\\
L\\
L\\
L\\
\hfill \mbox{\textit{SPS SPS SM 2021 Q5 [5]}}