Q. 2 I5.0( 1 Vote )

# Find the GCD of the following

24(6x^{4} – x^{3} – 2x^{2}),20(2x^{6} + 3x^{5} + x^{4})

Answer :

Given,

24(6x^{4} – x^{3} – 2x^{2}) = 2 × 2 × 2 × 3[x^{2}(6x^{2} – x – 2)]

= 2 × 2 × 2 × 3[x^{2}(6x^{2} – 4x + 3x – 2)]

= 2 × 2 × 2 × 3 × x^{2} [2x(3x – 2) + 1(3x – 2)]

= 2 × 2 × 2 × 3 × x^{2} (2x + 1)(3x – 2)

20(2x^{6} + 3x^{5} + x^{4}) = 2 × 2 × 5[x^{4}(2x^{2} + 3x + 1)]

= 2 × 2 × 5 × x^{2} × x^{2}[2x(x + 1) + 1(x + 1)]

= 2 × 2 × 5 × x^{2} × x^{2}(2x + 1)(x + 1)

Greatest common divisor = 2 × 2 × x^{2} × (2x + 1) = 4x^{2}(2x + 1)

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