Question: How to factorise the polynomial $p(x) = x^4-2x^3 + 2x - 1$.

Hence, solve the inequality $p(x) \gt 0$ ?

Answer: 
Draw $AD$. Then
$$ \angle BOD = 2\angle BAD = 2\angle PAD = 2(\angle ADC-\angle APD) = \angle AOC-2\angle APD = 7^\circ $$
Answer: $\angle BOD=7^o$

Proof:
Look at the triangle OAC. Then $\angle OAC=\angle OCA=\frac{137}{2}$.

Now, look at the triangle APC. Then $\angle OAP+ \angle OCP+137+18=180$. This implies that $\angle OAP+ \angle OCP=25^o$.

Look at the quadrilateral ABDC which is inscribed in a circle. Hence $180^o=\angle B+ \angle C=\angle OBA+ \angle OBD+\angle OCP+\frac{137}{2}=$

$\angle OAP+ \angle OBD+\angle OCP+\frac{137}{2}$. This implies that $\angle OBD=180-25-\frac{137}{2}$. Hence $\angle BOD=180-2\angle OBD=7^o$.