How do you factor #y= x^2 + 2x – 48#?

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Answer 1 · 2015-12-11T15:52:54

#color(blue)((x-6)(x+8) # is the factorised form of the expression.

#y=x^2+2x-48#

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 = 1*(-48) = -48#

AND

#N_1 +N_2 = b = 2#

After trying out a few numbers we get #N_1 = -6# and #N_2 =8#

#8*(-6) = -48#, and #8+(-6)= 2#

#y=x^2+color(blue)(2x)-48 =x^2+color(blue)(8x-6x)-48#

#=x(x+8) -6(x+8)#

#=color(blue)((x-6)(x+8) #