Answer :
Answer:
[tex](x^2 + 4)(x + 2)(x - 2)[/tex]
Step-by-step explanation:
Hello!
We can use the difference of square method.
Difference Of Squares (DOS)
The formula for the DOS is [tex](a + b)(a - b) = a^2 - b^2[/tex]
It is a simple way to factor polynomials.
The criteria:
- Has to begin and end with a perfect square
- The operation has to be subtraction
Factor:
- [tex]x^4 - 16[/tex]
Begins with a perfect square (x² * x²) and ends with a perfect square (4 * 4)
- [tex](x^2 + 4)(x^2 - 4)[/tex]
Warning! Watch out, there may be another DOS!
[tex]x^2 - 4[/tex] is another DOS
- [tex](x^2 + 4)(x + 2)(x - 2)[/tex]
The x² + 4 is not a DOS because the operation is addition.
The final factored form is [tex](x^2 + 4)(x + 2)(x - 2)[/tex]