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

Here is an example which does reduce. \[\frac{ x^2 - 2x +1 }{ x-1 }\]

Answer 2

How do we know that the binomial in the denominator is a factor of the polynomial in the numerator?

Answer 3

i dont know, can u help me? @RBauer4

Answer 4

We know because we can factor the numerator as see this fact. Look\[\frac{ x^2 - 2x +1 }{ x-1 } = \frac{ (x-1)(x-1) }{ x-1 }\]

Answer 5

yeah but how am i supposed to answer the question they asked?

Answer 6

They want you to give two example problems. One, like I gave you, should have a common factor between the numerator and denominator. The other, should not reduce; that is, the other should not have a common factor between the top and the bottom.

Answer 7

well How do you know if the binomial is a factor of the polynomial? @RBauer4

Answer 8

If it is a factor in the binomial expansion of the polynomial.