Question

Suppose you divide a polynomial by a binomial. How do you know if the binomial is a factor of the polynomial?
Create a sample problem that has a binomial which IS a factor of the polynomial being divided, and another problem that has a binomial which is NOT a factor of the polynomial being divided.

Answer 1

@The_Dahvie_Vanity

Answer 2

in polynomial division you know the binomial is a factor if there is no remainder

is the same rules as dividing numbers...

how many 3 in 12.... 4 no remainder, so 3 is a factor

Answer 3

so for you example keep it simple...

create a polynomial... which has zeros at x = 0, x = 1 and x = 2

P(x) = x(x-1)(x-2)

expand it out

then divide it by (x -1)

you should get the quotient as x^2 - 2x and no remainder

the no remainder means (x -1) is a factor... but you already know that.

use the same polynomial and divide it by (x + 1)

you will get a remainder..

hope it helps