Factor completely: 8+z^(6) Answer:

Question

Factor completely:  8+z^(6) Answer:

Bytelearn · Accepted Answer

Identify Expression Type: Step Title: Identify the Type of Expression Concise Step Description: Determine the type of expression to apply the correct factoring method. Step Calculation: The expression is of the form a + b^(2n), which resembles a sum of cubes when n is an odd integer. Here, z^(6) can be seen as (z^(3))^2, so we can consider the expression as a sum of squares. Step Output: The expression is a sum of squares.Apply Factoring Rule: Step Title: Apply the Sum of Squares Factoring Rule Concise Step Description: Since the sum of squares does not factor over the real numbers, we check if it can be factored over the complex numbers. Step Calculation: The sum of squares can be factored as (a + bi)(a - bi) over the complex numbers, where i is the imaginary unit. However, in this case, since we are looking for a complete factorization, we recognize that the sum of squares does not have a factorization in terms of real polynomials. Step Output: The expression 8 + z^(6) cannot be factored over the real numbers.

Factor completely: $\newline$ $8+z^{6}$ $\newline$ Answer:

Full solution

More problems from Factor polynomials

Related topics

Factor completely:\newline8+z6 8+z^{6} 8+z6\newlineAnswer:

Factor completely: $\newline$ $8+z^{6}$ $\newline$ Answer: