How do you factor #n^2+2n-15#?

Question

3313 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-30T10:48:00

We can Split the Middle Term of this expression to factorise it

In this technique, if we have to factorise an expression like #an^2 + bn + c#, we need to think of 2 numbers such that:

#N_1*N_2 = 1*-15 = -15#
AND
#N_1 +N_2 = b = 2#

After trying out a few numbers we get #N_1 = 5# and #N_2 =-3#
#5*-3= -15#, and #5+(-3)= 2#

#n^2+2n-15 = n^2 + 5n - 3n -15#

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

#(n+5)# is a common factor to each of the terms

#=color(green)((n+5)(n-3)#

Answer 2 · 2015-05-30T10:50:42

#n^2+2n-15#

By factorization:

#n^2+color(red)2ncolor(blue)[-15#

working #rArr -5+3=color(red)2, -5xx3=color(blue)[-15#

#n^2-5n+3n-15#

#n(n-5)+3(n-5)#

Answer :
#color(green)[(n+3)(n-5)#