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Complete Factoring

When factoring an expression, first check for a common factor, then check for a difference of squares, then for a perfect square trinomial, and then for a general trinomial.

Factor the expression 2x3 – 2x2 – 12x completely.

Solution: First check for a common factor: 2x is common to each term. Factoring 2x out of each term yields 2x(x2 – x – 6).


Next, there is no difference of squares, and x2 – x – 6 is not a perfect square trinomial since x does not equal twice the product of the square roots of x2 and 6.


Now, –3 and 2 are factors of –6 whose sum is –1.


Hence, 2x(x2 – x – 6) factors into 2x(x – 3)(x + 2).

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