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using the factor theorem, determine which of the following is a factor of the polynomial f(x)=x^3-4x^2+3x+2

User Ed Webb
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Let's use the factor theorem, which states that if a polynomial f(x) has a factor x - a, then f(a) = 0.

We can check each of the possible factors by plugging them into the polynomial and seeing if the result is zero:

- Let's try x = 1:

f(1) = (1)^3 - 4(1)^2 + 3(1) + 2 = 0

Since f(1) = 0, we know that x - 1 is a factor of f(x).

- Let's try x = -1:

f(-1) = (-1)^3 - 4(-1)^2 + 3(-1) + 2 = 6

Since f(-1) is not zero, we know that x + 1 is not a factor of f(x).

- Let's try x = 2:

f(2) = (2)^3 - 4(2)^2 + 3(2) + 2 = 0

Since f(2) = 0, we know that x - 2 is a factor of f(x).

- Let's try x = -2:

f(-2) = (-2)^3 - 4(-2)^2 + 3(-2) + 2 = -8 + 16 - 6 + 2 = 4

Since f(-2) is not zero, we know that x + 2 is not a factor of f(x).

Therefore, the factors of the polynomial f(x) are (x - 1) and (x - 2).

User Giorgio Robino
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