Mathematics, 27.04.2020 03:15 janahiac09

The polynomials f
x and g
x are defined by
f
x = x
3 + ax2 + b and g
x = x
3 + bx2 − a,

where a and b are constants. It is given that

x + 2 is a factor of f

x. It is also given that, when g
x

is divided by

x + 1, the remainder is −18.

(i) Find the values of a and b. [5]
(ii) When a and b have these values, find the greatest possible value of g
x − f
x as x varies.

Answers: 1

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The polynomials f
x and g
x are defined by
f
x = x
3 + ax2 + b and g