HCF and LCM

Find the HCF and LCM of 3x² + x -10,   6x² – x – 15 and 6x² -19x +15



Answer:

 3x² + x -10 =3x² +6 x- 5x -10 = 3x(x +2) - 5(x +2) = (3x - 5)(x + 2)

6x² – x – 15 = 6x² –10 x + 9x – 15  = 2x(3x - 5) + 3(3x - 5) = (2x + 3)(3x - 5)

 6x² -19x +15 = 6x² -10x - 9x +15 = 2x(3x - 5) -3(3x -5) = (2x - 3)(3x - 5)

The common factor is (3x -5). So, HCF = (3x - 5)

The LCM is (3x- 5)(x + 2)(2x + 3)(2x - 3)