How do you factor #2x^2+13x-24 #?

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Answer 1 · 2015-08-11T16:30:56

# color(blue)((2x-3)(x+8) # is the factorised form for the expression.

#2x^2 +13x -24#

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*-24 = -48#
and,
#N_1 +N_2 = b = 13#

After trying out a few numbers we get #N_1 = 16# and #N_2 =-3#

#16*-3 = -48#, and #16+(-3)= 13#

#2x^2 +color(blue)(13x) -24 = 2x^2 +color(blue)(16x - 3x) -24 #

# = 2x(x+8) - 3(x+8)#

# color(blue)((2x-3)(x+8) # is the factorised form for the expression.