Question

Find the HCF and LCM of 4x^2 - 36 ,2x^2 - 12x + 18 and 2x^2 + x - 21​

Answer 1

(x-3), 4 (x - 3)^2 (x + 3) (2 x + 7)

Explanation:

Factor all the expressions,

1st expression= 4x^2 - 36=4(x^2-9)=4(x+3)(x-3)

2nd expression=2x^2 - 12x + 18 =2(x^2-6x+9)=2 (x - 3)^2=2(x-3)(x-3)

3rd expression=2x^2 + x - 21​=(x - 3) (2 x + 7)

HCF=Commo factor=(x-3)

LCF=Common factor*Remaining factor=4(x+3)(x-3)(x-3) (2 x + 7)=4 (x - 3)^2 (x + 3) (2 x + 7)