Solve quadratics by inspection, square roots, completing the square, formula, and factoring; express complex solutions.
Solve a non-monic quadratic equation by factoring a trinomial and using the zero-product property
Problem
Solve \(2x^{2}+7x+3=0\) by factoring. Build binomial factors that reproduce the leading and constant terms, check the cross terms, and solve both factors.
Big Picture
What this problem is really about
Because the leading coefficient is not one, we’ll factor by splitting the middle term. We’ll find two numbers whose product is the leading coefficient times the constant and whose sum is the middle coefficient, regroup the four terms into a common-binomial product, and then solve both factors.
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