Interpolating polynomial Problem. Show that $p(3) = 1.25$

Question

My Question is:

Suppose that p(x) is the cubic polynomial that interpolates

.

in which $a ∈ [−2, 4].$

Show that $p(3) = 1.25$ in the case where $a = 0$

Ive been trying to do this question for a couple of hours but i seem to always get $3$ as my answer instead of $1.25.$ So if anyone could help me get to $1.25$ that would be appreciated.

Answer 1

$$L_0 = -\frac{1}{264}x(x-5)(x-8)$$ $$L_1 = \frac{1}{120}(x+3)(x-5)(x-8)$$ $$L_3 = \frac{1}{264}x(x+3)(x-5)$$ and you get $$p(3)=L_0+3L_1+0L_2+L_3=1.25$$

Wolframalpha link