Find the H.C.F. of the following :(i) x2 – 4 and x2 + 4x + 4(ii) 4

1.	Find the H.C.F. of the following :(i) x2 – 4 and x2 + 4x + 4(ii) 4x4 – 16x3 + 12x2 and 6x3 + 6x2 – 72x
Answer» (i) x² – 4 = (x + 2)(x – 2) x² + 4x + 4 = (x + 2)² H.C.F. of coefficient = 1 H.C.F. of other factors = (x + 2)¹ = x + 2 H.C.F. = x + 2 (ii) 4x⁴ – 16x³ + 12x² = 4x²(x² – 4x + 3) = 4x²(x – 1)(x – 3) 6x³ + 6x² – 72x = 6x(x² + x – 12) = 6x(x + 4)(x – 3) = 2x(x – 3) [because H.C.F. of coefficients is 2] = 2x² – 6x

Find the H.C.F. of the following :(i) x2 – 4 and x2 + 4x + 4(ii) 4x4 – 16x3 + 12x2 and 6x3 + 6x2 – 72x

Answer»

(i) x² – 4 = (x + 2)(x – 2)

x² + 4x + 4 = (x + 2)²

H.C.F. of coefficient = 1

H.C.F. of other factors = (x + 2)¹ = x + 2

H.C.F. = x + 2

(ii) 4x⁴ – 16x³ + 12x² = 4x²(x² – 4x + 3)

= 4x²(x – 1)(x – 3)

6x³ + 6x² – 72x = 6x(x² + x – 12)

= 6x(x + 4)(x – 3)

= 2x(x – 3) [because H.C.F. of coefficients is 2]

= 2x² – 6x