Q2 of 227 Page 89

Find the GCD of the following

24(6x4 – x3 – 2x2),20(2x6 + 3x5 + x4)

Given,


24(6x4 – x3 – 2x2) = 2 × 2 × 2 × 3[x2(6x2 – x – 2)]


= 2 × 2 × 2 × 3[x2(6x2 – 4x + 3x – 2)]


= 2 × 2 × 2 × 3 × x2 [2x(3x – 2) + 1(3x – 2)]


= 2 × 2 × 2 × 3 × x2 (2x + 1)(3x – 2)


20(2x6 + 3x5 + x4) = 2 × 2 × 5[x4(2x2 + 3x + 1)]


= 2 × 2 × 5 × x2 × x2[2x(x + 1) + 1(x + 1)]


= 2 × 2 × 5 × x2 × x2(2x + 1)(x + 1)


Greatest common divisor = 2 × 2 × x2 × (2x + 1) = 4x2(2x + 1)


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