How do you factor the expression d² + 2d - 15?

1 Answer
MeneerNask
Jan 25, 2016

You use the sum-product method, based on the expression:
#(x+a)(x+b)=x^2+(a+b)x+(a*b)#

Explanation:

First you factor #15#. This can be done in only two ways:
#15=1*15=3*5# (not looking at the signs yet).
Since the sum or difference between #1and15# are too great, we go for the second option.

Then you notice that the #15# has a #-#sign. This means that the factors have opposite signs, and we are looking for the difference between these signs.
So this could be #(-3and +5) or (+3and-5)#

Since the second term has a #+#sign it must be the first:

#=(x-3)(x+5)#

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