Express 6x^2 + 18x +6 in the form a(x - p)^2 +q?

Question

Please help me :'(

Answer 1

you can factor out a "6" from each term, right?

6x^2 + 18x + 6 = 6(x^2 + 3x +1) ....

But now how do you get (x^2 + 3x + 1)???

Well, (x-1)^2 = x^2 - 2x + 1.... but you have 3x as a middle term... so you have to add "+5x" to that.... because -2x + 5x = +3x

(x^2 - 2x + 1) + 5x = x^2 + 3x + 1 = (x-1)^2 + 5x

BUT ... THAT whole thing gets multiplied by "6"... so you have

6[(x-1)^2 + 5x].... But you want it in the form a(x-p)^2 + q.... so now distribute the 6 to each of the terms in the brackets [ ]'s....

6(x-1)^2 + 6(5x) = 6(x-1)^2 + 30x

so....

a = 6
x = x
p = 1
and q = 30x

6x^2 + 18x +6 = 6(x^2 + 3x +1) = 6[(x-1)^2 + 5x] = 6(x-1)^2 + 30x


HOPE THIS HELPS!!! =) And SMILE!!! I give you a star because this was a really great question to ask! It really makes you think! :o)