The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 5.13: FACTORING POLYNOMIALS BY FINDING

THE GREATEST MONOMIAL FACTOR

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To factor a polynomial by finding its greatest monomial factor, follow the steps below:

1. Find the greatest monomial factor of the polynomial.


2. Divide each term of the polynomial by the greatest monomial factor. (If 1 is the greatest
   monomial factor, the polynomial cannot be factored using this strategy.)


3. Write the product of the greatest monomial factor and the polynomial found in step 2.


4. Use the distributive property to check your work.

EXAMPLE

Factor 2 x^3 − 6 x^2 + 10 x.

The greatest monomial factor of the polynomial is 2x.

2 x^3

2 x

−

(

6 x^2

2 x

)

+

10 x

2 x

=x^2 − 3 x+ 5

2 x(x^2 −^3 x+5)=^2 x^3 −^6 x^2 +^10 x

DIRECTIONS: Factor each polynomial, if possible. If the polynomial cannot be factored,

write ‘‘cannot be factored.’’

1. 3 x+ 15 2. x^2 + 4 y


2. 8 ab− 3 ab^2 4. 20 x^2 y− 10 x+ 40 x^3


3. 49 x^2 −x 6. 35 x^4 y^3 − 15 x^2 y^5


4. a^2 b+ 2 a^3 b^2 8. 12 xy− 6 x^2

CHALLENGE:Eva factored 4x^2 y^2 − 10 xy^2 as 2xy(2xy− 5 y). Is she correct? If

not, explain why not and provide the correct answer.

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Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.