How do you factor the trinomial #6x^2-11x+3#?

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Answer 1 · 2016-05-14T07:01:38

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

#6x^2 - 11x + 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 = 6*3 = 18#

AND

#N_1 +N_2 = b = -11#

After trying out a few numbers we get #N_1 = -9# and #N_2 =-2#

# ( - 9 ) * ( - 2 ) = 18 #, and #(- 9) + ( - 2 )= -11#

#6x^2 - 11x + 3 = 6x^2 - 9x - 2x + 3 #

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

#(2x - 3 )# is a common factor to each of the terms

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