Is it possible to factor #y=x^2+5x-36#? If so, what are the factors?

1 Answer
May 1, 2018

Answer:

#y=x^2+5x-36# can be factored as #color(red)(""(x+9)) * color(blue)(""(x-5))#

Explanation:

Consider the generalized factoring:
#color(white)("XXX")color(red)(""(x+a))^2 * color(blue)(""(x+b))^2= x^2+(color(red)a + color(blue)b)x +(color(red)a * color(blue)b)#

Applying the right side to the given #x^2color(green)(+5)xcolor(magenta)(-36)#
we can see that we need two values #:color(red)a# and #color(blue)b#
such that
[1] their sum is #color(green)(+5)#, and
[2] their product is #color(magenta)(-36)#

Note that [2] implies that one of the numbers must be positive and the other negative (it's the only way you can get a negative product),
so we can think of the sum as being a difference of the magnitudes of the numbers (with the larger number being positive since #color(green)(+5)# is positive.

Checking possible factors of #color(magenta)(-36)# that meet the given requirements, we quickly find #color(red)(+9)# and #color(blue)(-5)#