Let p(x) be a monic polynomial of degree 4. Three of the roots of p(x) are 1, 2, and 3. Find p(0)+p(4).
Solution — click to reveal
Since three of the roots of p(x) are 1, 2, and 3, we can write p(x)=(x−1)(x−2)(x−3)(x−r).Then p(0)+p(4)=(−1)(−2)(−3)(−r)+(3)(2)(1)(4−r)=6r+24−6r=24.