Question

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Answer 1

x+2 is a binomial because it has two terms. It is also a polynomial.

Answer 2

Your question is confusing because the problems you have posted are division problems. The numerators are trinomials and the denominators are binomials

Answer 3

Could you please post the question EXACTLY as it is written?

Answer 4

If you divide and the remainder is 0 then the binomial is a factor of the polynomial.

Answer 5

Let's think about a numerical example. Is 4 a factor of 12?

Answer 6

How do you know?

Answer 7

Yes. It is a factor because 4 times 3 = 12.

Is 5 a factor of 12? No. Because there is no integer that makes this true: 5(?) =12

Answer 8

So let's extend this to polynomials.
(x+3)(x+2)= x^2+5x+6

So therefore (x^2+5x+6)/x+2= x+3 and

(x^2+5x+6)/x+3=x+2

Answer 9

Yes. Or you don't have to do the division if you do the factoring.

Answer 10

I can say that 4 is a factor of 12 by showing that 4 x 3 = 12. I don't have to do the division.

Answer 11

Similarly I can say that x+2 is a factor of x^2+5x+6 by showing that (x+2)(x+3)=x^2+5x+6

Answer 12

Let's not get all tangled up in the terminology. x^2+5x+6 is a trinomial. It is the result of multiplying two binomials. The two binomials are x+2 and x+3

Answer 13

All of them are polynomials

Answer 14

I know you are. That's why I wanted you to state your problem exactly as written so I could help you understand it.

Answer 15

Are you talking about your original post?

Answer 16

\[5^2-10x^2+7x^2=25-3x^2\]

Answer 17

10x^2 is not a factor of that binomial so I guess I don't understand what you are saying.

Answer 18

Do you have another problem you could post?