Solve quadratics by inspection, square roots, completing the square, formula, and factoring; express complex solutions.
Solve a monic quadratic equation by factoring the trinomial and using the zero-product property
Problem
Solve \(x^{2}+7x+12=0\) by factoring. Find two integers whose sum and product match the trinomial, write both linear factors, and use the zero-product property for the complete solution set.
Big Picture
What this problem is really about
A monic trinomial factors by finding two numbers whose product is the constant and whose sum is the linear coefficient. We’ll use that pair to write both binomial factors, verify the middle term, and apply the zero-product property to solve both linear equations rather than stopping after one factor.
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