Question

How do you factor `x^2-15x+50`?

Answer 1

`x^2-15x+50`

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*50 = 50`
and
`N_1 +N_2 = b = -15`

After trying out a few numbers we get `N_1 = -5` and `N_2 =-10`
`(-5)*(-10) = 50`, and `(-5)+(-10)= -15`

`x^2-15x+50 = x^2-5x - 10x +50`

`= x(x-5) -10(x-5)`
`= (x-10)(x-5)` , this is the factorised form.