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Question
In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not: (1−7)
f(x) = x3 − 6x2 + 11x − 6; g(x) = x − 3
Solution
Given that: `f(x) = x^3 - x^3 - 6x^2 + 11x - 6,`
`g(x)= x- 3,`
By the factor theorem,
If g(x) is a factor of f(x)
i.e. x - 3 =0
⇒ x = 3
Then
`f(3) = (3)^3 + 6(3)^2 + 11(3) - 6`
` = 27 - 54 + 33 - 6`
` = 60 - 60`
` = 0`
As f(3) is zero therefore g(x), is the factor of polynomial f(x).
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