Question 133
(A) Determine the value of the real number $k$ for which the polynomial $P(x) = x^3 - kx + 2$ has $2$ as root. For that value of $k$ write the polynomial $P(x) = x^3 - kx + 2$ as a product of two polynomials with integer coefficients.
(B) The positive real numbers $a, b$ satisfy the equation $2a + b + \frac{4}{ab} = 10$. Find the maximal value of $a$.
(B) The positive real numbers $a, b$ satisfy the equation $2a + b + \frac{4}{ab} = 10$. Find the maximal value of $a$.