Question

1. higher order thinking is it possible for the product of a monomial and trinomial to be a binomial? explain.

Explanation:

Step1: Define polynomial terms

A monomial is an algebraic expression with one - term (e.g., $3x$), a trinomial has three terms (e.g., $x^{2}+2x + 1$), and a binomial has two terms (e.g., $x + 1$).

Step2: Multiply monomial and trinomial

Let the monomial be $a$ and the trinomial be $b + c + d$. Then the product is $a(b + c + d)=ab+ac + ad$ which is a trinomial in general. But if one of the terms in the trinomial is $0$ or there is a cancellation. For example, if the monomial is $x$ and the trinomial is $x - x+1$, then $x(x - x + 1)=x\times1=x$ (a binomial since $x - x = 0$). Also, if the monomial is $x$ and the trinomial is $x^{2}-x^{2}+1$, $x(x^{2}-x^{2}+1)=x$.

Answer:

Yes, it is possible. This can happen when there is a cancellation of terms during the multiplication process, such as when two of the terms in the trinomial are additive inverses of each other.