MAT 095 Lecture 12: 4.6 Factoring A General Review Notes
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Provide a generalization to each of the terms listed in this section. Checking and factoring: check for all of the common factors, factor out all common factors out of the polynomial. Formulas: if there are no common factors, then you can check using one of the two following formulas for factorable polynomials. Y2 = (x y) (x + y) P roof : (x y) (x + y) = (x y) (x + y) = x (x) + x (y) + ( y) (x) + ( y) ( y) = x2 + (1 1) xy y2. Perfect square trinomial: a2 + 2ab + b2. F irst f ormula : a2 + 2ab + b2 = (a + b)2. = a (a) + a (b) + b (a) + b (b) = a2 + ab + ab + b2. = a2 + (1 + 1) ab + b2. 2ab + b2 = (a b)2.
