How do you factor the expression #4 a^2 -a - 5#?

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Answer 1 · 2016-03-16T12:39:55

#(4a - 5) ( a +1 ) # is the factorised form of the expression.

#4a^2−a−5 #

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #xa^2 + ya + z#, we need to think of 2 numbers such that:

#N_1*N_2 = x*y = 4*-1 = -4#

AND

#N_1 +N_2 = y= -1#

After trying out a few numbers we get #N_1 = -5# and #N_2 =4#

#4*-5 = -20#, and #4+(-5)= -1#

#4a^2−a−5 = 4a^2 + 4a−5a−5#

# = 4a( a +1 ) -5 (a+1)#

# = color(green)((4a - 5) ( a +1 ) #

#(4a - 5) ( a +1 ) # is the factorised form of the expression.