How do you factor the trinomial #6x^2 - 5x - 25#?

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Answer 1 · 2016-05-26T15:30:29

# color(blue)( (3x + 5 ) ( 2x - 5) # is the factorised form of the expression.

#6x^2 -5x -25#

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*(-25) = -150#

AND

#N_1 +N_2 = b = -5#

After trying out a few numbers we get #N_1 = -15# and #N_2 =10#

#10* (-15) = -150#, and #10+(-15)= -5#

#6x^2 -5x -25 = 6x^2 -15 x + 10x -25#

# = 3x ( 2x - 5) + 5 (2x -5)#

#(2x-5)# is a common factor to each of the terms:

# =color(blue)( (3x + 5 ) ( 2x - 5) #