How do you factor #5x^2 + 8x - 4#?

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Answer 1 · 2016-04-07T09:27:49

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

#5x^2 + 8x - 4#

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 = 5 * ( - 4) = -20#

AND

#N_1 +N_2 = b = 8#

After trying out a few numbers we get #N_1 = 10# and #N_2 =-2#
#10* (- 2) = -20#, and #10+(-2)= 8#

#5x^2 + 8x - 4 = 5x^2 + 10x - 2x - 4#

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

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

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

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