Roots and Zeros

Given a polynomial and one of its factors, find the remaining factors of the polynomial. Some of the factors may not be binomials.

One: 4x3 – 32x2 – 81x + 648; x – 8

Two: 64x3 – 528x2 – 1815x – 1331; x – 11

Solve the given equation. State the number and type of roots.

Three: x2 + 0x – 16 = 0

State the possible number of imaginary zeros in the given function.

Four: f(x) = -11x4 + 8x3 + 12x2 – 1x – 18

Five: f(x) = -13x3 + 1x2 + 11x8

Six:  Find all of the zeros of the function f(x) = x3 – 17x2 + 81x – 65.

Answers (  ONE: (2x – 9)(2x – 9)   TWO: (8x + 11)(8x + 11)   THREE: two real roots, 4 and -4   FOUR: 4   FIVE: 2   SIX: 1, (8 + i), (8 – i )

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