Find the GCD of $6 x^{3} - 30 x^{2} + 60 x - 48$ and $3 x^{3} - 12 x^{2} + 21 x - 18$ . [5 marks]

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Solution

Let, $f (x) = 6 x^{3} - 30 x^{2} + 60 x - 48 = 6 (x^{3} - 5 x^{2} + 10 x - 8)$ and $g (x) = 3 x^{3} - 12 x^{2} + 21 x - 18 = 3 (x^{3} - 4 x^{2} + 7 x - 6)$
Now, we shall find the GCD of $x^{3} - 5 x^{2} + 10 x - 8$ and $x^{3} - 4 x^{2} + 7 x - 6$
(1 mark)
(2 marks)
GCD of leading coefficients 3 and 6 is 3 .
Thus, GCD $[(6 x^{3} - 30 x^{2} + 60 x - 48, 3 x^{3} - 12 x^{2} + 21 x - 18)] = 3 (x - 2)$ .
(2 marks)

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