Finding constants?

Question

Been given some maths homework and it asks the questions:

Find the constants of a and b such that, for all values of x,
x^2 + 4x + 14 = (x + a)^2 + b

and

You are given that f(x) = x^3 - 7x + 6
1 Show that (x-2) is a factor of f(x)
2 Solve the equation f(x) = 0

I have no idea how to do these and I would really appreciate if someone could possibly post a walkthrough to the solution or just a walkthrough so I can attempt it myself, either one's good.

Thanks :)

Answer 1

completing the square
x^2+4x+14 = (x+2)^2 +10 so a=2 and b=10
by synthetic division
x^3-7x+6=(x-2)(x^2+2x-3)
so one root is x=2 and
x^2 +2x-3= 0 so x=((-2+-(4)/2 so x= -3 and x= 1