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.

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

Answer 1

use the remainder theorem

which requires you to evaluate P(2)

if P(2) = 0 then 2 is a zero... otherwise its not a root.

Answer 2

Is it supposed to equal zero or -2?

Answer 3

what did you get when you substituted 2?

Answer 4

I got -2

Answer 5

great I got the same... so using the remainder theorem since P(2) does not equal 0 you can say that 2 is not a zero.

and its a simple way to test the possible zeros of a polynomial

Answer 6

Thank You For Helping(:

Answer 7

The remainder theorem also tells you, in this case, that the remainder of
\[\Large 2x^3 – 5x^2 + 4x – 6\] is -2, when you divide that function by x-2, (since 2 is a zero). You could check it with synthetic or long division.

Answer 8

Thank You (:

Answer 9

That should say (since you're checking if 2 is a zero, so you divide by x-2)