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

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