Question

11)

Answer 1

Answer:

The factorization of given expression $x^2 + 81$ is (x + 9i)(x – 9i) and option d is correct.

Solution:

Given, expression is $x^2 + 81$

We have to factor it in the complex numbers.

Let us check options to find answer.

A) (x – 9)(x – 9)  

(x – 9)( x – 9)  $=(x-9)^{2}=x^{2}-18 x+81$

So, this is not correct answer.

B) (x + 9)(x + 9)  

$(x+9)(x+9)=(x+9)^{2}=x^{2}+18 x+81$

So, this is not correct answer.

C) (x + 9i)(x + 9i)

$(x+9 i)(x+9 i)=(x+9 i)^{2}=x^{2}+18 x i+81(-1)=x^{2}+18 x i-81$

So, this is not correct answer.

D) (x + 9i)(x - 9i)

$(x+9 i)(x-9 i)=x^{2}-(9 i)^{2}=x^{2}-(-81)=x^{2}+81$

Thus option D is correct

Hence, the factorization of given expression is (x + 9i)(x – 9i). and option d is correct.