QuestionChallenge \#17: Factor $6 M^{2}-7 M-5$ three different ways.

Studdy Solution
Rewrite the polynomial in factored form using the completed square.
$$6(M - \frac{7}{12})^2 - \frac{169}{24} = 6(M - \frac{7}{12})^2 - \frac{169}{24}$$
Factoring this form is less straightforward, but the goal here is primarily to show a different approach. The polynomial is already factored in the form of a perfect square minus some constant.
SOLUTION: The polynomial $6M^2 - 7M - 5$ can be factored in the following ways:
1. By grouping: $(2M + 1)(3M - 5)$
2. Using the quadratic formula: $(2M + 1)(3M - 5)$
3. Completing the square: The result is not a simple binomial product, but the completed square form is useful for understanding the structure.