FINDING GCD OF POLYNOMIALS BY LONG DIVISION WORKSHEET

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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