How do you factor x^2 +3x - 18 = 0x2+3x−18=0?

1 Answer
Don't Memorise
May 23, 2015

x^2 + 3x -18x2+3x−18

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 + cax2+bx+c, we need to think of 2 numbers such that:

N_1*N_2 = a*c = 1*(-18) = -18N1⋅N2=a⋅c=1⋅(−18)=−18
and,
N_1 +N_2 = b = 3N1+N2=b=3

After trying out a few numbers we get N_1 = 6N1=6 and N_2 =-3N2=−3
6*(-3) = -186⋅(−3)=−18 and 6+(-3)= 36+(−3)=3

x^2 + 3x -18 = x^2 + 6x - 3x -18x2+3x−18=x2+6x−3x−18

x(x+6) -3(x+6)x(x+6)−3(x+6)

color(green)((x-3)color(red)((x + 6)(x−3)(x+6) is the factorised form.

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