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15 April, 14:19

Xavier said the product of a monomial and a binomial will always be a trinomial. Explain the error in his reasoning.

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  1. 15 April, 15:44
    0
    See below.

    Step-by-step explanation:

    Each term in the binomial (there are 2 terms, by definition) is multiplied by the single term (monomial) so the answer will be another binomial.

    For example:

    2x (x - 6)

    = 2x^2 - 12x.
  2. 15 April, 16:00
    0
    All that is needed is a single counter-example.

    One counter-example is to multiply the monomial x^3 with the binomial x^7-10x^4

    We then get ...

    x^3 * (x^7-10x^4) = x^3*x^7 + x^3 * (-10x^4)

    x^3 * (x^7-10x^4) = x^10 - x^7

    The result we get is a binomial as there are still only two terms here. We would need three terms to have a trinomial.
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