How do you factor #6x^2 + 5x +1#?

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Answer 1 · 2015-09-23T12:52:20

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

#6x^2 +5x+1#

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 = 6*1 = 6#
AND
#N_1 +N_2 = b = 5#

After trying out a few numbers we get #N_1 = 2# and #N_2 =3#
#2*3 =6# and #2 + 3 = 5#

#6x^2 +color(blue)(5x)+1 = 6x^2 +color(blue)(2x+3x) +1#

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

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