Question

Factor the polynomial completely.

Answer 1

Answer:

The factors of the polynomial: (b⁴ - 2)(b² - 3)

Step-by-step explanation:

The given polynomial is: $\textbf{b}^{\textbf{6}} \textbf{-3b}^{\textbf{4}} \textbf{-2b}^{\textbf{2}} \textbf{+ 6}$

We can factor the given polynomial by grouping.

We get: $\{ b^6 - 3b^4\} + \{2b^2 + 6\}$

$= b^4 (b^2 - 3) -2(b^2 - 3)$

Taking (b² - 3) common outside, we get:

$= \{b^2 - 3\} \{b^4 - 2\}$

Hence the polynomial $b^6 - 3b^4 - b^2 + 6$ can be factored as $(b^4 - 2)(b^2 - 3)$.

Hence, the answer.