Question

@nincompoop could you help me with this?

Part 1: 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

If the binomial is a factor of the polynomial, then there will be no remainder. Let's look at this in simple numbers:

7/2
Here, think of 7 as the polynomial and 2 as the binomial.
We will get 3 remainder 1 as the answer. Therefore, 2 is not a factor of 7.

Answer 2

ok. now one more thing. arent polynomials and binomials the same thing?

Answer 3

Well, they're not exactly the same. You see, a binomial is a type of polynomial. A binomial is a polynomial that has two terms, such as 6x - 3 or 7x - 2. A polynomial is a general term that refers to a monomial, binomial, trinomial, etc.

Answer 4

ok. so how would you divide a polynomial by a binomial if a binomial is a type of polynomial?

Answer 5

I don't see why you can't :). An example of polynomial/binomial is below.

\[4x^2 + 5x - 8 \div 4x - 3\]

Answer 6

wait. so it doesnt matter which polynomial you use to divide with the binomial?

Answer 7

Nope :).

Answer 8

oh. ok. starting to make sense now.

Answer 9

um yes. so an example of this would be something like 14/7 right?

Answer 10

I don't get you. Are you trying to ask if that is a polynomial/binomial?

Answer 11

The 7 wouldn't be a binomial; it is a monomial.

Answer 12

ok but that pretty much the idea right? a polynomial that goes into a binomial.

Answer 13

Yes, that's the idea.

Answer 14

all i can pretty much do right now is think of 14 and 7 im that tired.

Answer 15

Well, whichever polynomial you think of, remember that a binomial has two terms. Good luck!

Answer 16

ok. thank you so much for helping me.

Answer 17

You're welcome.