DIRECTIONS: Factor each trinomial completely The word or phrase next to the equivalent expression w complete the statement correctly if it cannot be factored, the answer is "not factorable" \( 3 d^{2}-4 d-7 \) Yunus was offered a Fulbnght Scholarship and earned a Ph D. in economics at \[ \begin{array}{l}\text { (3d + 1)(d - 7) Belmont College } \\ \text { (d - 1) }(3 d+7) \text { Loyola University } \\ \text { (d }+1)(3 d-7) \text { Vanderbit University }\end{array} \]
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This trinomial \( 3d^{2}-4d-7 \) can be neatly factored using the method of grouping or trial and error along with the quadratic formula for precision. After testing possible factor pairs that maintain the product of the outer terms and the inner terms, you get \( (3d + 1)(d - 7) \) as the correct factorization! For some historical context, quadratic equations have been studied for thousands of years, dating back to Ancient Babylon. They used geometric methods to solve these equations long before the symbolic notation we use today was invented. So next time you factor a trinomial, remember you’re tapping into a rich tradition that spans millennia! Also, when factoring polynomials, a common mistake is forgetting to check if your factors multiply back to the original trinomial. After you factor, it’s always good practice to redistribute (FOIL) your factors to ensure they equal the original expression. Keep that mistake at bay for smoother sailing in your math journey!