How do you factor completely #x^2+11x+30#?

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Answer 1 · 2016-04-22T16:42:26

#color(green)((x + 6)( x +5)# is the factorised form of the expression.

#x^2 + 11x + 30#

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

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

#N_1*N_2 = a*c = 1* 30 = 30 #

AND

#N_1 +N_2 = b = 11#

After trying out a few numbers we get #N_1 = 5# and #N_2 =6#
#5*6 = 30#, and #5 + 6 = 11#

#x^2 + 11x + 30 = x^2 + 5x + 6x + 30#

# = x ( x + 5) + 6 (x +5)#

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

#=color(green)((x + 6)( x +5)#