When factoring a trinomial, why is it necessary to write the trinomials in four terms?"

You keep posting this without any thinking.

Can this be factored in four terms?
10x^5 + 2x + 17

Perhaps you are meaning factoring the "quadratic" (a polynomial of degree 2) equation. Often a quadratic equation is a trinomial. The reason for that is that the degree 2 solution always involves two solutions, so...
(x-a)(x-b)=0 is the only way to get two solutions.

I still don't understand?
Yes I have been thinking alot on this one...i am just not understanding it

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dude its 2018

I'm sorry if my previous response was not clear. Let me try to explain again.

When factoring a trinomial, it is not always necessary to write it in four terms. In fact, many trinomials can be factored into two binomial terms. However, if you are asked to factor a trinomial into four terms, it is usually because the trinomial cannot be factored directly into two binomials. By expanding the trinomial into four terms, it allows us to break it down further and find its prime factors.

For example, let's consider the trinomial:

10x^5 + 2x + 17

To factor this into four terms, we first look for the common factors among the coefficients. In this case, there are no common factors.

Then, we look for any possible factors of the leading term (10x^5) and the constant term (17). In this case, there are no factors of 10x^5 and 17 other than 1 and themselves.

Next, we consider the linear term (2x). We try to find two binomial terms that, when multiplied, give us this linear term. In this case, there are no such binomials.

Therefore, we can conclude that the trinomial 10x^5 + 2x + 17 cannot be factored further into two binomials or any other combination of terms. So, in this case, it is not necessary to write it in four terms.

I hope this explanation helps clarify the concept of factoring trinomials for you. If you have any further questions, please let me know. Additionally, if you need help with writing or speaking English, I'm here to assist you with that as well. Just let me know what specific areas you would like to work on, and I will provide guidance and resources.