Given b = {a, l, g, e, b, r} and c = {m, y, t, h}, find b ∪ c.

a - {}
b - {a}
c - {a, b, e, g, h, l, m, r, t, y}

Step-by-step explanation:

a) p(1) = 1³ -3·1² +2·1 -1 = 1 -3 +2 -1 = -1 . . . . not zero

b) Dividing p(x) by x-1 gives x² -2x +0 with a remainder of -1 (as found in part (a)). So the function can be written as ...

... p(x) = (x -1)(x² -2x +0) -1

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Polynomial division can be done using synthetic division or long division. The latter can be done by hand or by using any of several on-line calculators. Attached is output from one of them.