Part 1: Determine whether 2 is a zero of the polynomial P(x) = 2x3 – 5x2 + 4x – 6 by using the Remainder Theorem. Show your work. (4 points)

Part 2: Explain how the Remainder Theorem is useful in finding the zeros of a polynomial function. (4 points)

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Question

Part 1: Determine whether 2 is a zero of the polynomial P(x) = 2x3 – 5x2 + 4x – 6 by using the Remainder Theorem. Show your work. (4 points) 

Part 2: Explain how the Remainder Theorem is useful in finding the zeros of a polynomial function. (4 points)
  
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campbell_st · Answer

use the remainder theorem 

which means substituting 2 into the polynomial. If you have a zero remainder, then 2 is a factor. 

$$P(2) = 2\times(2)^3 - 5\times(2)^2 + 4\times(2) - 6$$