Question

Select the correct answer. Which expression is equivalent to this polynomial? x2 + 8

Answer 1

Answer:

D ( x -2i sqrt(2)) ( x+ 2i sqrt(2))

Step-by-step explanation:

x^2 + 8

We want to factor so rewrite as squares

x^2 + (2sqrt(2))^2

Rewrite with a subtraction sign i^2 = -1

x^2 - (2*i*sqrt(2))^2

This is the difference of squares

a^2 - b^2 = ( a-b) (a+b)

( x -2i sqrt(2)) ( x+ 2i sqrt(2))

Answer 2

Answer:

Option D is the correct answer

Step-by-step explanation:

$(x + 2 \sqrt{2} i)(x - 2 \sqrt{2} i) \\ \\ = ( {x})^{2} - {(2 \sqrt{2}i )}^{2} \\ \\ = {x}^{2} - {2}^{2}. {( \sqrt{2} )}^{2} {i}^{2} \\ \\ = {x}^{2} - 4.2( - 1) \\( \because \: {i}^{2} = - 1) \\ \\ = {x}^{2} + 8$