Use the Factor Theorem to determine whether x-2 is a factor of P(x)= x^4-2x^3+3x-6.

Specifically, evaluate P at the proper value, and then determine whether x-2 is a factor.

Question

Use the Factor Theorem to determine whether x-2 is a factor of P(x)= x^4-2x^3+3x-6.

Specifically, evaluate P at the proper value, and then determine whether x-2 is a factor.

jim_thompson5910 · Answer

Hint: if you can show that P(2) = 0, then you will have shown that x - 2 is a factor

anonymous · Answer

Hm, I'm reading the example in the book, trying to see how to show that and uuhhhh math is not my strong point.

jim_thompson5910 · Answer

P(x)= x^4-2x^3+3x-6

P(2)= (2)^4-2(2)^3+3(2)-6

P(2) = ??

anonymous · Answer

wait, i think i get it now...hold on

jim_thompson5910 · Answer

ok

anonymous · Answer

It's true p=0. You were telling me to plug 2 for x  with the hint and i just didn't get it. Sometimes I have to see it...lol

anonymous · Answer

p(2)=2^4-2*2^3+2-6
2P=16-16+6-6
2p=0

jim_thompson5910 · Answer

yes so because P(2) = 0, this means x-2 is a factor of P(x) by the factor theorem

jim_thompson5910 · Answer

no you leave it as P(2) 

that's not the same as 2P

anonymous · Answer

Sorry, typing fast.

anonymous · Answer

Thank you!

jim_thompson5910 · Answer

you're welcome