Question

The expression x - 2 is a factor of p(x) = x^5 - 4x^3 + 2x^2 - 4x + 1. TRUE or FALSE?

Answer 1

Use the idea that if x - k is a factor of p(x), then p(k) = 0 (this is part of the remainder theorem)

Answer 2

If you can show that p(2) = 0, then x - 2 is a factor of p(x)

Answer 3

My answer is False. Am I correct?

Answer 4

what is p(2)

Answer 5

I think it's 0?

Answer 6

p(x) = x^5 - 4x^3 + 2x^2 - 4x + 1

p(2) = (2)^5 - 4(2)^3 + 2(2)^2 - 4(2) + 1

p(2) = ???

Answer 7

-2

Answer 8

which calculator are you using?

Answer 9

a regular calculator.

Answer 10

graphing calculator? like TI-83?

Answer 11

no. the regular calculator that comes on a pc

Answer 12

oh gotcha, I'd use graphcalc or google as a calculator

you can type in (2)^5 - 4(2)^3 + 2(2)^2 - 4(2) + 1 exactly as you see it into google

Answer 13

google will then compute that as a calculator would

Answer 14

wolfram alpha also does the same

Answer 15

1

Answer 16

P(2) = 1

because P(2) does not equal zero, this means x - 2 is not a factor

Answer 17

I said it was False earlier

Answer 18

but it's handy to know how/why it's false

Answer 19

and to know how to compute function values as well

Answer 20

Thank you .

Answer 21

you're welcome