How do you factor r^2 + (6/4r) + (9/16)?

How fractions get factored?

1 Answer
Vocaloid
May 15, 2018

#(r+3/4)^2#

Explanation:

Start by finding two numbers (let's call them #a# and #b#) such that:

#a*b = 9/16#
#a+b=6/4#

This requires a bit of guess-and-checking but we can propose that a and b are equal and check if it works:

#a*a=9/16#
gives #a=3/4 and b = 3/4# which just happens to satisfy the second requirement as well
#3/4 + 3/4=6/4#
making the factored form equal to #(r+3/4)^2#

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