HCF and LCM

1. Find the HCF of 2x²  x  1 and 4x²  8x  3             3

2. Find the HCF of x²  x  2andx3  4x²  x  6             4

3. For what value of r, the HCF of x²  x  2r  2 and2x²  rx  12is x  4?             3

4. Find r if x . r is HCF of x² . x . 6 and x² + 3x . 18.             3

5. Find the HCF of x³ + 2x² . 3x and 2x² + 5x² . 3x.             4

6. Find the LCM of 9x² (x + 4) (x . 4)⁴ and 17x⁵ (x + 4) (x . 3)³             3

Find the HCF and LCM of polynomials given below. Verify that the product of LCM and HCF differs the product of polynomials if at all by a factor of -1 (for question 7 and 8)

7. 1 . x2 and x3 . 1             4

8. (5x . 1)3 (4x . 9)2 and (5x . 1)2 (4x . 9)4             4

9. Find the values of r and s so that f(x) = 3x3 + rx2 . 13x + s is divisible by x² . 2x . 3             4

10. Find LCM of polynomials 2y² . 8, 3y² . 9y + 6 and 6y² + 18y + 12            4

11. x . 1 and x3 + 5x2 . x . 5 are respectively the HCF and LCM of two quadratic polynomials. Find them.             4