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3 years ago

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

Mathematics

2 answers:

sergejj [24]3 years ago

5 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.

drek231 [11]3 years ago

4 0

Answer:

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.

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