How do you factor #-2x ^ 2 + 7x -3?

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Answer 1 · 2015-05-07T05:03:54

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 = 7#

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

#6*1 = 6#, and #6+1= 7#

#-2x ^ 2 + 7x -3 = -2x^2 +6x + x - 3#

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

#x-3# is a common factor to each of the terms

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