Factor out the greatest common factor in the given polynomial. (See Example 1.)r3 − 5r2+ r...

Factor out the greatest common factor in the given polynomial. (See Example 1.)

r3 − 5r2+ r

Example 1

Factor out the greatest common factor.

(a) 12p − 18q

Solution Both 12p and 18q are divisible by 6, and

 

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(b) 8x3 − 9x2 +15x

Solution Each of these terms is divisible by x:

 

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(c) 5(4x − 3)3 + 2(4x − 3)2

Solution The quantity (4x − 3)2 is a common factor. Facturing it out gives