x^2−2x- 8 = 0x2−2x−8=0
We can Split the Middle Term of this expression to factorise it and thereby find the solutions:
In this technique, if we have to factorise an expression like ax^2 + bx + cax2+bx+c, we need to think of 2 numbers such that:
N_1*N_2 = a*c = 1*-8 = -8N1⋅N2=a⋅c=1⋅−8=−8
AND
N_1 +N_2 = b = -2N1+N2=b=−2
After trying out a few numbers we get N_1 = -4N1=−4 and N_2 =2N2=2
2*(-4) = -82⋅(−4)=−8 and 2 + (-4)= -22+(−4)=−2
x^2−2x- 8 = x^2 color(blue)(- 4x + 2x)- 8x2−2x−8=x2−4x+2x−8
= x( x-4) + 2(x - 4)=x(x−4)+2(x−4)
color(blue)((x+2) ( x-4)(x+2)(x−4) is the factorised form for the expression, we now equate the factors to zero and obtain the solutions.
x+2 = 0, color(blue)(x=-2x+2=0,x=−2
x-4 = 0, color(blue)(x=4x−4=0,x=4
