Answer:
f(x) = x² -3x +2
Explanation:
We know from the first point that (x -2) is a factor of the polynomial, so we can write the other factor as (ax+b). Filling in the values from the other two given points, we have ...
f(x) = (x -2)(ax +b)
f(3) = (3 -2)(3a +b) = 2
f(4) = (4 -2)(4a +b) = 6
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From the first of these, ...
3a + b = 2
Dividing the second by 2, we have ...
4a + b = 3
Subtracting the first of these equations from the second gives ...
(4a +b) -(3a +b) = (3) -(2)
a = 1
Using this in the first of the above equations, we have ...
3·1 + b = 2
b = -1
Then the factored form of the equation is ...
f(x) = (x -2)(x -1)
Expanding this to standard form, we have ...
f(x) = x² -3x +2