Which of the following are binomials? check all that apply. a. x b. -x^10 c. x^7 d. x^2+18 e. x+ 3/x f. x+2

If these are your answer choices:     then the only answers are    x² + 18 and x + 2======a binomial is just a polynomial with two terms.a polynomial is defined so that all the variable terms have whole number  exponents {0,1,2,3,} and all coefficients are real numbers. the number of terms in a polynomial can be found after full simplification (combining like terms). the terms are separated by "+" and "-".therefore, if something is not a polynomial, then it can not be a binomial.let's go through every choice.choice " a. x " is a polynomial but it only has one term. it would be a monomial, not a binomial.choice " b. -x¹⁰ " is a polynomial but it only has one term. it would be a monomial, not a binomial.choice " c. x⁷ " is a polynomial but it only has one term. it would be a monomial, not a binomial.choice " d. x² + 18 " is a polynomial with two terms, so it is a binomial.choice " e. x + 3/x " is not a polynomial because the is an x in the denominator. the x in the denominator implies that we can write it as x + 3x⁻¹. since the exponent -1  is not a whole number ( -1  not in the set of whole numbers  {0,1,2,} ), choice e is not a polynomial and therefore can't be classified as a binomial.choice " f. x + 2 " is a polynomial with two terms, so it is a binomial.the answers are  x² + 18  and  x + 2.

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