How do you factor w squared minus 13w plus 48?

Answer 1

w2 - 13w + 48

You want to write the equation in the form (w+a)(w+b). However, if this particular equation could be written in this form, there would be at least one value of x where y = 0. There are no such solutions for this equation, so it cannot be factored into this form.
However, you can factor it if you separate 48 into 42.25 + 5.75:
w2 - 13w + 48 = (w - 6.5)2 + 5.75 = (w - 6.5)(w - 6.5) + 5.75