A Polynomial is defined as X^3-6X^2+11X-6. a)i Use the factor theorem to show that X-3 is a factor. ii Express as a linear and quadratic b)Find the first and second derivative c) Prove there is a maximum at y=0.385 to 3DP

a)i Factor Theorem states that if a polynomial has a factor of X-a, when a is substituted in, the polynomial = 0. Therefore substitute 3 into the polynomial, which then equals 0 ii Long Devision- Unsure how to write this, but can explain it. b)Just differentiation, so multiply by the power and then minus 1 c) Maximum has a gradient of 0 and the second derivative must be <0. By making the first derivative equal to 0, we can find the points where the gradient is equal to 0 by solving it. Then substituting the two answers into the second derivative allows us to know which is a maximum. Finally, substitute it back into the polynomial, which should get 0.385