Solve inequality involving polynomial

A question is this type if and only if you must solve p(x) > 0 or p(x) < 0 by first factorising the polynomial and analysing sign changes.

1 questions · Standard +0.3

1.02g Inequalities: linear and quadratic in single variable 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

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CAIE P3 2022 November Q2

6 marks Standard +0.3

2 The polynomial \(2 x ^ { 3 } - x ^ { 2 } + a\), where \(a\) is a constant, is denoted by \(\mathrm { p } ( x )\). It is given that ( \(2 x + 3\) ) is a factor of \(\mathrm { p } ( x )\).

Find the value of \(a\).
When \(a\) has this value, solve the inequality \(\mathrm { p } ( x ) < 0\).