How do you factor the expression #x^2 - 7x - 18#?

Question

↳Redirected from "How do the valence electrons change as you go across a period?"

32094 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-05T17:08:13

#(x-9)(x+2)#

#Step 1:#
Look for two numbers(#a# and #b#) whose product is #-18# and whose sum is #-7#.
That is, #axxb = -18# and #a+b = -2#

To find those numbers write down the factors of #-18# which are: #{-1,1,-2,2,-3,3,-6,6,-9,9,-18,18}#

Now you will need some intuition to see that #-9xx2 = -18#
and #-9+2 = -7#

So the two numbers are #-9# and #2#.

#Step 2:#
Write down the second term of the expression(#7x#) as a sum of two terms whose coeficients are the two numbers we have found above.

#x^2-7x-18 rarr x^2+2x-9x-18#

#Step 3:#
Write down the factor out the first two terms and the two other terms.

#x^2+2x-9x-18 rarr x(x+2)-9(x+2)#

#Step 4:#
You remain with two terms(#x(x+2)# and #-9(x+2)#)
which can further be factored, like this

#x(x+2)-9(x+2) rarr color(blue)((x+2)(x-9))#

Which cannot be further factored.