To solve this question, we use the factor theorem, and using it, the polynomial function is:

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The factor theorem means that if k is a root of f(x), f(k) = 0.
Thus, applying the factor theorem for this question, we have to choose the function for which: 
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Function 1:

Testing the values:



Thus, since all three conditions are satisfied,
is the polynomial function.
A similar question is given at brainly.com/question/11378552
P=2*(l+w)
p=2l+2w
2w=p - 2l
w= (p-2l)/2
Y = -(1/2)(x-2)² +8
Re write it in standard form:
(y-8) = -1/2(x-2)² ↔ (y-k) = a(x-h)²
This parabola open downward (a = -1/2 <0), with a maximum shown in vertex
The vertex is (h , k) → Vertex(2 , 8)
focus(h, k +c )
a = 1/4c → -1/2 = 1/4c → c = -1/2, hence focus(2, 8-1/2) →focus(2,15/2)
Latus rectum: y-value = 15/2
Replace in the equation y with 15/2→→15/2 = -1/2(x-2)² + 8
Or -1/2(x-2)² +8 -15/2 = 0
Solving this quadratic equation gives x' = 3 and x" = 2, then
Latus rectum = 5
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Step-by-step explanation: