Question on Algebra

Question

Let $P(x)$ be a fourth degree polynomial with coefficient of leading term be $1$ and $P(1) = P(2) = P(3) = 0$, then find the value of $P(0) + P(4)$ .

An even worse title would be "Question about mathematics". – Pierre Arlaud May 21 '14 at 12:57 — Pierre Arlaud, May 21 '14 at 12:57

score 10 · Accepted Answer · answered May 21 '14 at 07:02

10

Hint: as the coefficient term is 1 $$P(x)=(x-1)(x-2)(x-3)(x-a)$$, then $$P(0)+P(4)=6a+6(4-a)$$.

answered May 21 '14 at 07:02

enigne

1

I think it's worth noting that $P(0) + P(4) = 6a + 6(4-a) = 24$, independent of $a$. Right idea, though, so +1. – Robert Lewis May 21 '14 at 07:23

1 Answers1