How do you factor #3y^2 +13y + 4#?

1 Answer
Feb 26, 2016

Answer:

#color(blue)((3y+1) (y+4) # is the factorised form of the equation.

Explanation:

#3y^2 +13y +4#

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

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

#N_1*N_2 = a*c = 3*4 = 12#

AND

#N_1 +N_2 = b = 13#

After trying out a few numbers we get #N_1 = 12# and #N_2 =1#
#12*1 = 12#, and #12+ 1= 13#

#3y^2 +13y +4 =3y^2 +12y +y +4 #

#=3y (y+4) + 1 (y+4)#

#(y+4)# is a common factor to each of the terms.
#=(3y+1) (y+4)#

#color(blue)((3y+1) (y+4) # is the factorised form of the equation.