How do you factor # 2x^2 - 5x - 3#?

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Answer 1 · 2016-04-03T10:58:52

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

#2x^2 - 5x - 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 = 2 *(- 3) = - 6#

AND

#N_1 +N_2 = b = -5#

After trying out a few numbers we get #N_1 = -6 and #N_2 =1#

#1*(-6) = -6#, and #1+(-6)= -5#

#2x^2 color(blue)( - 5x) - 3 = 2x^2 color(blue)( - 6x + 1x) - 3#

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

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

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