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November 8th, 2018, 01:27 AM   #1
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Factor Trinomials Of The Form Ax2 + Bx + C Using Trial And Error.

In the OpenStax Elementary Algebra book in the section on factoring using Trial and Error, there is the following paragraph.

"When we factor an expression, we always look for a greatest common factor first. If the expression does not have a greatest common factor, there cannot be one in its factors either. This may help us eliminate some of the possible factor combinations."

Then there is Example 7.25 which asks the question:

Factor completely: 14x^2 − 47x − 7

It then lists possible factors but dismisses some without checking if they are valid e.g. (x + 1)(14x - 7). Besides the ones it dismisses, it says:

"if the trinomial has no common factors, then neither factor can contain a common factor. That means each of these combinations is not an option."

Could someone expand on this explanation as I don't get what they mean?

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November 8th, 2018, 03:40 AM   #2
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The second factor in (x + 1)(14x - 7) has 7 as a common factor of its terms, but 7 isn't a common factor of the trinomial's terms.

14x² − 47x − 7 = (7x + 1)(2x - 7)
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