If f (x) and g(x) are two polynomials of same degree then the polynomial carrying the highest coefficient will be the dividend.
In case, if both have the same coefficient then compare the next least degree’s coefficient and proceed with the division.
If r (x) = 0 when f(x) is divided by g(x) then g(x) is called GCD of the polynomials.
(1) Find the GCD of the given polynomials
(i) x4 + 3x3 −x −3, x3 +x2 −5x + 3 Solution
(ii) x4 - 1, x3 - 11x2 + x - 11 Solution
(iii) 3x4 + 6x3 −12x2 −24x, 4x4 +14x3 + 8x2 −8x Solution
(iv) 3x3 + 3x2 + 3x + 3 , 6x3 +12x2 + 6x +12 Solution
(2) Find the LCM of the given expressions.
(i) 4x2y, 8x3y2 Solution
(ii) -9a3b2, 12a2b2c Solution
(iii) 16m, -12m2n2, 8n2 Solution
(iv) p2 − 3p +2, p2 - 4 Solution
(v) 2x2 - 5x -3, 4x2 -36 Solution
(vi) (2x2 -3xy)2, (4x -6y)3, 8x3 -27y3 Solution
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