1.
Answer all the questions.
$$f ( x ) = 3 x ^ { 3 } - 7 x ^ { 2 } + 7 x - 10$$
- Use the factor theorem to show that ( \(x - 2\) ) is a factor of \(\mathrm { f } ( x )\)
- Find the values of the constants \(a , b\) and \(c\) such that
$$\mathrm { f } ( x ) \equiv ( x - 2 ) \left( a x ^ { 2 } + b x + c \right)$$
- Using your answer to part (b) show that the equation \(\mathrm { f } ( x ) = 0\) has only one real root.
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