Respuesta :

chetankachana

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]

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