Question

11)

- Factor x2 +81 in the complex numbers.
A)
(X - 9)(x - 9)
B)
(x + 9)(x + 9)
(x + 90)(x + 91)
D)
(x + 91)(x-91)

Answer 1

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.