RELATION BETWEEN GCD AND LCM OF POLYNOMIALS PRACTICE QUESTIONS

(1)  Find the LCM of each pair of the following polynomials

(i)  x²-5x+6, x²+4x-12 whose GCD is (x-2)

Solution

(ii)  x⁴+3x³+6x²+5x+3, x⁴+2x²+x+2 whose GCD is x²+x+1

Solution

(iii)  2x³+15x²+2x-35, x⁴+8x²+4x-21 whose GCD is x+7

Solution

(iv)  2x³-3x²-9x+5, 2x⁴-x³-10x²-11x+8 whose GCD is 2x-1

Solution

(2)  Find the other polynomial q(x) of each of the following, given that LCM and GCD and one polynomial p(x) respectively.

(i)  (x+1)² (x+2)², (x+1) (x+2), (x+1)² (x+2)

Solution

(ii)  (4x+5)³ (3x-7)³, (4x+5) (3x-7)², (4x+5)³ (3x-7)²

Solution

(iii)  (x⁴-y⁴)(x⁴+x²y²+y⁴), x²-y², x⁴-y⁴      Solution

(iv)  (x³-4x) (5x+1), (5x²+x), (5x³-9x²-2x)     Solution

(vi)  2(x+1) (x²-4), (x+1), (x+1) (x-2)     Solution

(v)  (x-1) (x-2) (x²-3x+3), (x-1), (x³-4x²+6x-3)

Solution

(vi)  2(x+1) (x²-4), (x+1), (x+1) (x-2)        Solution

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