Common Factors Exercises

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Pull out and cancel the common factor 4 for .

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Pull out and cancel the common factor 5x for .

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The common factor is 11xy. Canceling gives us

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That numerator is the problem: 3x⁴ + 6x² – 3x = 3x(x³ – 2x – 1), not 3x(x² – 2x). Looks like someone forgot a few terms.

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We're not allowed to cancel the x² and 2x terms that way. In order to cancel them, common factors must be factors of every term in both the numerator and denominator of the rational expression. Just because something looks like it should work a certain way doesn't mean that's the case. Try telling that to your grandmother and her TV remote.

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The student didn't pull out all the common factors. A factor of y can still be yanked from each term, to give . Why'd they overlook y? Tough to say, but it's probably some deep-rooted psychological issue. Maybe a y stole their lunch money.