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Answer:
f(x) = -x^2 +8x -16
Step-by-step explanation:
With the given data, we can write the factored function as ...
f(x) = -1(x -4)^2 . . . . . -1 is the leading coefficient; exponent of 2 gives root multiplicity
f(x) = -x^2 +8x -16
Because it show the relationship between the x and y coordinates
X is the length
y is the width
2x+2y=66
x-y=15
multiply the second equation by 2 (elimination)
2x-2y=30
add the equations together
4x=96
x=24
Plug this in to one of the original equations
24-y=15
the width is 9
The factor theorem says that for a function f(x), if f(a) = 0, then (x - a) is a factor of f(x).
For f(x) = 2x^4 + 22x^3 + 60x^2
f(-5) = 2(-5)^4 + 22(-5)^3 + 60(-5)^2 = 2(625) + 22(-125) + 60(25) = 1250 - 2750 + 1500 = 0
Therefore, x - (-5) = x + 5 is a factor of f(x).
