SOLUTION: Factor by grouping if possible: 2x^2-8x+xy-4y Factor completely: x^2-x-20 36x^2-y^2 x^2+22x+121

Question 268547: Factor by grouping if possible:
2x^2-8x+xy-4y
Factor completely:
x^2-x-20
36x^2-y^2
x^2+22x+121
Answer by persian52(161) (Show Source): You can put this solution on YOUR website!
2x^(2)-8x+xy-4y
Factor the greatest common factor (GCF) from each group.
(2x(x-4)+y(x-4))
Factor the polynomial by grouping the first two terms together and finding the greatest common factor (GCF). Next, group the second two terms together and find the GCF. Since both groups contain the factor (x-4), they can be combined.
(2x+y)(x-4)
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x^(2)-x-20
For a polynomial of the form x^(2)+bx+c, find two factors of c (-20) that add up to b (-1). In this problem 4*-5=-20 and 4-5=-1, so insert 4 as the right hand term of one factor and -5 as the right-hand term of the other factor.
(x+4)(x-5)
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36x^(2)-y^(2)
The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).
(6x-y)(6x+y)
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x^(2)+22x+121
For a polynomial of the form x^(2)+bx+c, find two factors of c (121) that add up to b (22). In this problem 11*11=121 and 11+11=22, so insert 11 as the right hand term of one factor and 11 as the right-hand term of the other factor.
(x+11)(x+11)
Combine the two common factors of (x+11) by adding the exponents.
(x+11)^(2)
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