2.4: Evaluation and linear factorisation

0606/21/O/N/20 — Question 7 · 6 marks

Do not use a calculator in this question.

The polynomial p(x)=2x3−3x2−23x+12p(x) = 2x^{3} - 3x^{2} - 23x + 12.
(a)
Find the value of p ⁣(12)p\!\left(\tfrac{1}{2}\right).
[1]
(b)
Write p(x)p(x) as the product of three linear factors and hence solve p(x)=0p(x) = 0.
[5]