Question

Factor completely x2 + 64.

(x + 8)(x − 8)
Prime
(x + 8)(x + 8)
(x − 8)(x − 8)

Answer 1

this cannot be factored using real numbers.
a^2 - b^2 = (a-b)(a+b)
a^2 + b^2 = (a-bi)(a+bi)
so your best bet is
x^2 + 64 = (x-8i)(x+8i)

better review the topic.

Answer 2

Solve equation:

x² + 64 = 0

Subtract 64 to both sides

x = - 64

x = ± √- 64 = ± √ 64 ∙ ( - 1 ) = ± √ 64 ∙ √ - 1 = ± 8 i

The solutions are:

x = 8 i and x = - 8 i

Each quadratic equation can be written in the form:

a x² + b x + c = a ( x - x1 ) (x - x2 )

where x1 and x2 are the roots of this quadratic equation

In this case a = 1

so

x² + 64 = 1 ∙ ( x - 8 i ) [ x - ( - 8 i ) ] = ( x - 8 i ) ( x + 8 i )

Answer 3

so the answer to choose would be "prime"