(Make sure to set f(x) to zero)
So for this equation, I will be factoring by grouping. Firstly, what two terms have a product of -5x^2 and a sum of 4x? That would be 5x and -x. Replace 4x with 5x - x: [tex]0=5x^2+5x-x-1[/tex]
Next, factor 5x^2 + 5x and -x - 1 separately. Make sure that they have the same quantity on the inside: [tex]0=5x(x+1)-1(x+1)[/tex]
Now you can rewrite the equation as: [tex]0=(5x-1)(x+1)[/tex]
Now apply zero product property to the factors to solve for x:
[tex]5x-1=0\\5x=1\\x=\frac{1}{5}\\\\x+1=0\\x=-1[/tex]
The x-intercepts are (1/5 ,0) and (-1,0).
