Problem 6 [Polynomial functions] Let 𝑃(𝑥) = 𝑥 5 − 5𝑥 4 + 𝑎𝑥 3 + 14&#1199

[answerhappygod]

Problem 6 [Polynomial functions] Let 𝑃(𝑥) = 𝑥 5 − 5𝑥 4 + 𝑎𝑥 3 +
14𝑥 2 − 3𝑥 + 𝑏. Justify all your answers. (a) If 𝑃(𝑥) has zeros
(roots) 𝑥 = 1 (with multiplicity 1) and 𝑥 = 3 (with multiplicity
2), find constants 𝑎 and 𝑏. (b) Use the result of (a) to factor
𝑃(𝑥) completely. (c) Find all real zeros of the polynomial 𝑃(𝑥).
(d) When the polynomial P(x) is divided by D(x) = 2𝑥 − 2, find the
quotient Q(x) and the remainder R using polynomial division and
write it as P(x) = D(x)Q(x) + R. (e) Sketch the graph of the
polynomial 𝑃(𝑥).