Algebra
posted by Jason on .
For what real number k does 3x^2 k factor as
3(x 2)(x + 2)?
Can someone please help with this question? I can not understand how it says to solve this in the book

Y = 3X^2 + K
Vertex Form:
Y = a(X h)^2 + k
= 3(X 0)^2 + K
Y = 3(X2)(X+2),
= 3(X^2 4)
= 3X^2  12
h = b / 2a = 0 / 6 = 0.
K = Yv = 3*0^2 12 = 12. V(0 , 12).
Let's use a positive 2 in the 1st
parenthesis of our factored Eq.
Y = 3(X + 2 )(X + 2) = 3(X + 2)^2 =
3(X^2 + 4X + 4) = 3X^2 + 12X + 12.
h = Xv = b / 2a = 12 / 6 = 2.
This value of h does not agree with
our given Eq in which h = 0.
Therefore, 2 is the correct choice.