How do you factor #4x^2 + 24x + 11#?

1 Answer
May 19, 2015

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 = 4*11 = 44#
AND
#N_1 +N_2 = b = 24#
After trying out a few numbers we get #N_1 = 2# and #N_2 =22#
#2*22 = 44#, and #2+22= 24#

#4x^2 + 24x + 11 = 4x^2 + 2x + 22x + 11#

# = 2x(2x+1) + 11(2x+1)#

#(2x+1)# is a common factor to each of the terms

#=color(green)((2x+1)(2x+11)#