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Chapter: 10th Mathematics : Algebra

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Exercise 3.2: GCD and LCM of Polynomials

Maths Book back answers and solution for Exercise questions - (Greatest Common Divisor (GCD) or Highest Common Factor (HCF) of Polynomials, Least Common Multiple (LCM) of Polynomials)

Exercise 3.2


1. Find the GCD of the given polynomials

(i) x 4  + 3x 3 − x − 3, x 3 + x 2 − 5x + 3

(ii) x 4 -1 , x 3 − 11x 2 + x −11

(iii) 3x 4  + 6x 3 −12x 2 − 24x, 4x 4 + 14x 3 + 8x 2 − 8x

(iv) 3x 3 + 3x 2 + 3x + 3 , 6x 3 + 12x 2 + 6x + 12



2. Find the LCM of the given expressions.

(i) 4x 2y, 8x 3y2

(ii) -9a 3b2, 12a 2b2c

(iii) 16m, -12m 2n2, 8n2

(iv) p 2 − 3 p + 2, p2 – 4

(v) 2x 2 - 5x - 3, 4x 2 – 36

(vi)  (2x 2  - 3xy)2, (4x - 6y)3, 8x 3 - 27y3



Answers:

1.(i) 2 + 2 (ii)  x 21  (iii) x (2  + 4+ 4) (iv) 3(x 21)

2.(i) 8x 3y(ii) –36a3b2(iii) -48m 2n2

(iv) ( p  1) ( p  2)( p + 2) (v) 4(x + 3)(2x + 1) (x - 3)

(vi) 3 x 2 (2x  3y )3 (4x 26xy + 9y2 )

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