How do you factor the trinomial #2y^2 + 6y − 20#?

1 Answer
Tony B
Nov 26, 2015

#(2y+10)(y-2)#

Explanation:

For #2y^2# we can only have:

#(2y+?)(y+?)#

It is just a matter of finding the other two for -20

Target Factors of 20#-> color(green)({1,20}, {2, 10} {4,5})#

Testing the factors:
#+-(color(blue)(2y)xxcolor(green)(?))+-(color(blue)(1y)xxcolor(green)(?))=6# for #6y#

#(y)color(white)(..........)(y)#
#+-color(brown)((color(blue)(2)xxcolor(green)(2))+-(color(blue)(1)xxcolor(green)(10))) -> +-(4)+-(10)-> -4+10=6 color(white)(..)color(red)("works")#

Check

#=> (2y+10)(y-2)#

#=2y^2-4y+10y-20#

#=2y^2+6y-20 #

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