(m-4)(m^2+4m-5)

Jasonbradley

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Jun 16, 2024

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Factoring the Expression (m-4)(m^2+4m-5)

This expression represents a product of two factors:

• (m - 4): This is a simple binomial.
• (m^2 + 4m - 5): This is a quadratic trinomial.

To fully simplify the expression, we need to factor the quadratic trinomial.

Factoring the Trinomial

We can factor the trinomial by finding two numbers that:

• Multiply to give -5 (the constant term).
• Add up to 4 (the coefficient of the middle term).

These two numbers are 5 and -1. So, we can rewrite the trinomial as:

(m^2 + 4m - 5) = (m + 5)(m - 1)

Final Result

Now, we can substitute the factored trinomial back into the original expression:

(m - 4)(m^2 + 4m - 5) = (m - 4)(m + 5)(m - 1)

Therefore, the fully factored form of the expression (m - 4)(m^2 + 4m - 5) is (m - 4)(m + 5)(m - 1).