Given h(x)=x+2 and x^2-4 is h(x) a factor of f(x)?

Question

 need help asap

Answer 1

The factor theorem states that a polynomial f(x) has a factor (x-k) if and only if f(k)=0, [i.e.  k is a root] -- Wikipedia

 

Multiplying factors produces a term.

Polynomial f(x) = x²-4
        f(x) = (x+2)(x-2)                [use F-O-I-L to verify this]
                    ^                   [ (x+2) is a factor ]

Factor:   h(x) = x+2                [given]
             h(x) = x - (-2)
           k = -2

Is h(x) a factor of f(x)?   Well, if and only if f(-2)=0      [note: k=-2, so (x-k)=(x+2) ]
      f(x) = (x+2)(x-2) = 0   

    Is    f(-2) = 0   ?

           f(-2) = (-2+2)(-2-2)   ?     [plug in value of x]
           f(-2) = (0)(-4)   ?
            f(2) = 0   ?    [yes; (x+2) is a factor; x=-2 is a root]

Answer 2

X^2-4=(x+2)(x-2), so x+2 is the factor.