Practice Makes Perfect by Carolyn Wheater

Author:Carolyn Wheater
Language: eng
Format: epub
Publisher: McGraw Hill LLC
Published: 2022-06-15T00:00:00+00:00

Greatest common monomial factor

You will often be able to find several different factor pairs for a monomial. You know this is true when you factor a constant, but it’s also true for a single term involving a variable. The constant 24 could be factored as 1 × 24, 2 × 12, 3 × 8, or 4 × 6. The monomial could be written as and more.

Identifying the GCF

The greatest common monomial factor of a polynomial is the largest monomial that is a factor of every term. In this context, largest means the “largest coefficient and the highest power of the variable.” The polynomial 10x3y3 has a greatest common factor (GCF) of because 2 is the largest integer that divides all three coefficients, x3 is the largest power of x present in all terms, and y is the largest power of y present in all terms. Notice that the largest power of a variable contained in all the terms is the smallest one you see. The largest power of x in is x3, which is the smallest power of x in any of the terms. You can leave the extra variables behind, but you can’t factor out more than the monomial has.

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