Problem 6 [Polynomial functions] Let P(x) = x5 - 5x4 + ax3 + 14x2 – 3x + b. Justify all your answers. (a) If P(x) has ze

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Problem 6 Polynomial Functions Let P X X5 5x4 Ax3 14x2 3x B Justify All Your Answers A If P X Has Ze 1 (29.75 KiB) Viewed 28 times

Problem 6 [Polynomial functions] Let P(x) = x5 - 5x4 + ax3 + 14x2 – 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).