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Product-Sum Method for Factoring Quadratics

Select the PRODUCT and SUM for the quadratic you wish to factor. The graphs for those two criteria are shown, and the two numbers are represented by the intersection points of the two graphs.
Write three possible PRODUCT-SUM combinations where: a) the two numbers are integers (i.e. they have no decimals) b) the two numbers are rational numbers (i.e. they have decimals) c) when one of the two numbers is zero d) there are not two numbers that meet those criteria (i.e. the graphs don't intersect) Draw the picture for the following special polynomials: a) difference of squares (A²-B²)=(A+B)(A-B) b) trinomial square (A±B)²=A²±2AB+B² c) sum of squares (A²+B²) which is not factorable