Factor completely x2 + 64.
(x + 8)(x − 8)
Prime
(x + 8)(x + 8)
(x − 8)(x − 8)
To factor the expression x^2 + 64 completely, we first need to apply the difference of squares formula. The difference of squares formula states that a^2 - b^2 can be factored as (a - b)(a + b).
In this case, the expression is x^2 + 64, and we can view 64 as 8^2. So, we can rewrite the expression as x^2 - 8^2.
Now, we can use the difference of squares formula to factor it completely:
x^2 - 8^2 = (x - 8)(x + 8).
Therefore, the expression x^2 + 64 can be factored completely as (x - 8)(x + 8).
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 )
so the answer to choose would be "prime"
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.