True or false,  adding polynomials will always yield a polynomial answer. If false correct the underline words (polynomial answer).

Expert Answers

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This is true: the result of adding two polynomials will always be another polynomial.

A polynomial is an algebraic expression made up of the sum of monomials, which are products of numbers (coefficients) and variables in positive integer exponents.

For example, `2x^3` is a polynomial of one term (monomial),

`x^2 - 4` is a polynomial of two terms (binomial),

`3x^4 + x^2 - 1` is a polynomial of three terms (trinomial).

When adding polynomials, the result will be the sum of all the terms of each polynomial. Sometimes, when the polynomial terms contain the same variable in the same exponent (like terms), these terms will combine and produce one term. Thus, the number of terms in the resultant polynomial may vary.

For example, addition of the binomial and trinomial above results in

`(x^2 - 4) + (3x^4 + x^2 - 1) = 3x^4 + 2x^2 - 5` 

Here, the "x square" terms and constant (number) terms combine, so the result is a trinomial.

In a very special case, when the two polynomials being added are opposites of each other, all their terms will cancel and the result will be 0. For example,

adding `x^4- x` and `x-x^4` will result in 0. However, 0 is also technically a polynomial with one term, or monomial.

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