2. (a) The polynomial p(x) = x⁴ - 3x³ + ax² + bx - 10 has (x - 1) and (x + 2) as factors. Find the values of the constants a and b. [6 marks]

(b) Using the values of a and b found in (a), factorize p(x) completely. [5 marks]

(c) Hence, express (3x³ - 4x² - 17x + 18) / p(x) in partial fractions, given that (x - 1) is a repeated factor in the denominator after full factorization. [9 marks]

Question

2. (a) The polynomial p(x) = x⁴ - 3x³ + ax² + bx - 10 has (x - 1) and (x + 2) as factors. Find the values of the constants a and b. [6 marks]

(b) Using the values of a and b found in (a), factorize p(x) completely. [5 marks]

(c) Hence, express (3x³ - 4x² - 17x + 18) / p(x) in partial fractions, given that (x - 1) is a repeated factor in the denominator after full factorization. [9 marks]

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