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Step 1:I'll solve this step-by-step using the guidelines you specified:
Step 2:: Identify the structure of the quadratic expression
• Here, $$a = 1$$, $$b = -4$$, and $$c = -12
• This is a quadratic expression in standard form: ax^{2} + bx + c
Step 3:: Determine the method of factoring
2) Add up to $$b$$ (in this case, $$-4$$)
• We'll use the method of finding two numbers that:
Step 4:: Find the two numbers
-6 + 2 = -4
• We need two numbers that:
Step 5:: Rewrite the middle term using these numbers
• $$x^{2} - 6x + 2x - 12
Step 6:: Group the terms
• $$(x^{2} - 6x) + (2x - 12)
Step 7:: Factor out common terms from each group
• $$x(x - 6) + 2(x - 6)
Step 8:: Factor out the common binomial
• $$(x - 6)(x + 2)
Final Answer
x^{2} - 4x - 12 = (x - 6)(x + 2)
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