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math:common_factorizations [2020/11/03 23:28] – created epixmath:common_factorizations [2020/11/03 23:43] (current) epix
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 ===== Perfect Square Trinomial ===== ===== Perfect Square Trinomial =====
 $x^2 + bx + c = (x + \frac{b}{2})^2$ where $ \sqrt{c} = \frac{b}{2}$ $x^2 + bx + c = (x + \frac{b}{2})^2$ where $ \sqrt{c} = \frac{b}{2}$
 +===== Grouping =====
 +This one is a bit difficult to describe, so an example would do best.
 +  - $x^3 - 3x^2 - x + 3$ //example quadratic//
 +  - $x^3 - 3x^2$ **//__plus__//** $-x + 3$ //group terms with common factors//
 +  - $x^2(x - 3)$ **//__plus__//** $-1(x - 3)$ //reverse distribute common factors//
 +  - $(x^2 - 1)(x - 3)$ //reverse distribute the common group//((Remember that the equation really looks like $x^2(x - 3) + -1(x - 3)$, if you get confused by how there is a common factor between the groups))

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