Question

Determine whether 2 is a zero of the polynomial P(x) = 3x3 – 6x2 – 3x – 18 by using the Remainder Theorem. Explain how the Remainder Theorem is useful in finding the zeros of a polynomial function.

Answer 1

P(x) = 3x3 – 6x2 – 3x – 18 using the remainder theorem
P(2) = 3(2)^3 – 6(2)^2 – 3(2) – 18
p(2)=-24 the remainder r=-24 if you divide 3x3 – 6x2 – 3x – 18 by x-2

Answer 2

3x^2 -3
- ------------------
x-2/3x^3 – 6x^2 – 3x – 18
-(3x^3 -6x^2)
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-3x-18
-(-3x+6)
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-24=R