Name DateWORKSHEET 5.17: FACTORING BY GROUPING
-------------------------------------------------------------------------------------Some polynomials that have four terms may be factored by grouping terms that have
common factors. Follow the steps below:- Group the four terms into two groups so that each group has a common monomial
factor. - Factor the greatest monomial factor of each binomial. A binomial that is a common
factor should result. - Factor out the binomial that is a common factor.
- Check by multiplying the factors.
EXAMPLE
Factorxy+ 2 x+ 5 y+ 10 by grouping.(xy+ 2 x)+(5y+10) or (xy+ 5 y)+(2x+10)x(y+2)+5(y+2) or y(x+5)+2(x+5)
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(y+2)(x+5) or (x+5)(y+2)
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(y+2)(x+5)+yx+ 5 y+ 2 x+ 10 or (x+5)(y+2)+xy+ 2 x+ 5 y+ 10DIRECTIONS: Factor by grouping.
- xy+ 3 x− 2 y− 6 2. xy+ 2 x− 3 y− 6 3. 3 xy− 2 + 2 y− 3 x
- xy− 7 x+ 3 y− 21 5. xy− 4 x+ 3 y− 12 6. x^2 y+ 2 y+ 2 x^2 + 4
- x^2 − 4 x− 2 xy+ 8 y 8. x^2 y− 4 xy− 3 x+ 12 9. 2 xy− 6 x−y+ 3
CHALLENGE:Miguel tried to factor 2x^2 −x− 20 x+10 by grouping. He
rewrote the polynomial as (2x^2 +10)−(x+20) and factored 2(x^2 +5)−
(x+20). He said that the binomials in parentheses are different and
therefore could not be factored by grouping. His teacher said that the poly-
nomial could be factored by grouping. Who is correct? Explain your answer.209Copyright
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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.