How do you factor completely #2x^2-x-10#?

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Answer 1 · 2016-05-23T13:11:39

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

#2x^2 - x - 10#

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 = 2*(-10) = -20#

AND

#N_1 +N_2 = b = -1#

After trying out a few numbers we get #N_1 = -5# and #N_2 = 4#
#4* (-5) = -20#, and #4+(-5)= -1#

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

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

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

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