This is the answer in the book but I don't know how they got from
well, you can use the quadratic formula to find the roots of the equation, which the roots are
[-b+sqrt(b^2-4ac)]/2a and [-b-sqrt(b^2-4ac)]/2a
where a=1, b=-5root(2), c=12
after you get the roots, rewrite your equation in the form of
First note that . That means that in order to factor a polynomial of the form you look for numbers and such that and . In this particular example and so you need to solve and . Since that product does NOT have a in it, it is clear that both and must have a factor of .
So, now, we are thinking and for some numbers m and n. and so we now have m+ n= 5 and mn= 6. -2 and -3 satisfy those equations so we can take and and have