Binomials and trinomials are two types of polynomials. The first has two terms and the second has three.
A trinomial is a polynomial with three terms.
Trinomials are polynomials with three terms. ie. x2+2x+1
Terms in polynomials are simply separated by a plus or minus sign. For example, if you had: x+12x, that would be a binomial (two terms). A trinomial is when the expression has three or more terms, 7x+12x-6x.
Polynomials have terms, but not sides. One with exactly three terms is a "trinomial". Polygons have sides. One of those with exactly three sides is a "triangle".
A binomial is an algebraic expression of the sum or the difference of two terms. A polynomial is an expression of more than two algebraic terms, esp. the sum of several terms that contain different powers of the same variable(s). The degree of a polynomial is the highest degree of its terms. Now that we have the definitions and the correct spellings out of the way, the answer to your question is a qualified no. There's no such thing as a second-term polynomial. I suspect you mean second degree, but both binomials and polynomials can be second-degree. There's also no such thing as a binomial polynomial. Expressions of two terms are binomials, more than two terms are polynomials, exactly three terms are trinomials.
A trinomial is a polynomial. All trinomials are polynomials but the opposite is not true. a trinomial= three unlike terms. a polynomial= "many" unlike terms.
Monomial consisting of one term ( 3x ) , Binomial consisting of two terms ( x + y ), Trinomial consisting of three terms ( 3x+4x+5xy ), and Multinomial consisting of three or more terms.
To multiply TWO polynomials, you multiply each term in the first, by each term in the second. This can be justified by a repeated application of the distributive law. Two multiply more than two polynomials, you multiply the first two. Then you multiply the result with the third polynomial. If there are any more, multiply the result with the fourth polynomial, etc. Actually the polynomials can be multiplied in any order; both the communitative and associate laws apply.
First off, it is NOT A QUINTIC! Typically a polynomial of four or more terms is called "a polynomial of n terms", where n is the number of terms. Only the one, two, and three term polynomials are referred to by a particular naming convention.
The sum of two polynomials is always a polynomial. Therefore, it follows that the sum of more than two polynomials is also a polynomial.