Find the highest

(i) Let u(x) = a³b⁴

Let v(x) = ab⁵

Let w(x) = a²b⁸

By comparing all the above equations, we get,

HCF = ab⁴ (Least power of a and b)

(ii) Let u(x) = 2⁴ × x² × y²

Let v(x) = 2⁴ × 3 × x⁴ × z

By comparing all the above equations, we get,

HCF = 2⁴ × x²

= 16 x² (Least power of x, y and z and also common terms of u(x) and v(x))

(iii) Let u(x) = x² – 7x + 12

= x² – 4x – 3x + 12

= x(x – 4) – 3(x – 4)

= (x – 3) (x – 4)

Let v(x) = x² – 10x + 21

= x² – 7x – 3x + 21

= x(x – 7) – 3(x – 7)

= (x – 7) (x – 3)

Let w(x) = x² + 2x – 15

= x² + 5x – 3x – 15

= x(x + 5) – 3(x + 5)

= (x – 3) (x + 5)

By comparing all the above equations, we get,

HCF = (x + 3) [only common term from u(x), v(x) and w(x)].

(iv) Let u(x) = (x + 3)² (x – 2)

Let v(x) = (x + 3) (x – 2)²

By comparing all the above equations, we get,

HCF = (x + 3) (x – 2) [Least power and common term from u(x) and v(x)].

(v) Let u(x) = (8 × 3) (6x⁴ – x³ – 2x²)

= (8 × 3) x² (6x² – x – 2)

= (8 × 3) x² (6x2 – 4x + 3x – 2)

= (8 × 3) x² (2x (3x – 2) + 1(3x – 2))

= (8 × 3) x² (2x + 1) (3x – 2)

Let v(x) = 20(6x⁶ + 3x⁵ + x⁴)

= (4 × 5) x⁴(6x² + 3x + 1)

= (4 × 5) x⁴(6x² + 3x + 1)

By comparing all the above equations, we get,

HCF = 4 x² (2x + 1) [Least power and common term from u(x) and v(x)].