How do you factor #3x^2+7x+2#?

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Answer 1 · 2016-05-16T17:10:39

# color(green)((3x + 1 ) (x + 2)# is the factorised form of the expression.

#3x^2 + 7x + 2 #

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 = 3*2 = 6#

AND

#N_1 +N_2 = b = 7#

After trying out a few numbers we get #N_1 = 6# and #N_2 =1#

#6*1 = 6#, and #6 + 1 = 7#

#3x^2 + 7x + 2 = 3x^2 + color(blue)( 6x + 1 x ) + 2 #

# = 3x(x + 2) + 1 (x + 2 )#

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

# = color(green)((3x + 1 ) (x + 2)#