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29 March, 12:47

Create a trinomial where the GCF of the trinomial is 5m^3

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  1. 29 March, 13:29
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    5m^5 + 15m⁴ + 35m³

    Step-by-step explanation:

    GCF means greatest common factor.

    The Greatest common factor of two monomials for example, is the product of the common prime factors of both monomials.

    We are to develop a trinomial which would have 5m³ as its greatest common factor.

    To Create a trinomial where the GCF of the trinomial is 5m³, we would find a trinomial that can't be factored and multiply it by 5m³.

    A trinomial is a polynomial which has three terms (monomials) connected by addition or subtraction.

    Let's consider the trinomial m² + 3m + 7

    This trinomial cannot be factored because there are no common factors between them. The constants to be considered are 3 and 7.

    3 is a prime number and therefore can only be factored to 1 and 3.

    7 is a prime number and therefore can only be factored to 1 and 7.

    Since there are no common factors other than 1, the constants cannot be factored.

    By multiplying 5m³ with the trinomial m² + 3m + 7

    We would have:

    5m³ (m² + 3m + 7) = 5m^5 + 15m⁴ + 35m³

    From the above, the trinomial where the GCF of the trinomial is 5m³ = 5m^5 + 15m⁴ + 35m³
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