Question

(ii) f(x) = x4 – 27a3x = x(x3 – (3a)3)
g(x) = (x – 3a)2
G.C.D = (x – 3a)

Answer 1

Step-by-step explanation:

Correct option is

A

x−3a

We first factorize x

4

−27a

3

x and (x−3a)

2

as shown below:

x

4

−27a

3

x

=x(x

3

−27a

3

)

=x[x

3

−(3a)

3

]

=x[(x−3a)(x

2

+(3a)

2

+(x×3a)]

=x(x−3a)(x

2

+9a

2

+3ax)

(x−3a)

2

=(x−3a)(x−3a)

The common factor of x

4

−27a

3

x and (x−3a)

2

is (x−3a), therefore, the GCD is x−3a.

Hence, the greatest common divisor of x

4

−27a

3

x and (x−3a)

2

is x−3a.