How do you factor #3x^2+10x+3#?

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Answer 1 · 2015-08-10T15:32:54

#color(blue)((3x+1)(x+3)# is the factorised form for the expression.

#3x^2 +10x +3#

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*3 =9#
and,
#N_1 +N_2 = b = 10#

After trying out a few numbers we get:
#N_1 = 9# and #N_2 =1#
#9*1 = 9#, and #9+(1)= 10#

#3x^2 +color(blue)(10x) +3 = 3x^2 +color(blue)(9x+1x) +3#
#=3x(x+3)+1(x +3)#

#color(blue)((3x+1)(x+3)# is the factorised form for the expression.