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A polynomial has a leading coefficient of 1 and the
following factors with multiplicity1:
x-(2 + i)
X - V2
What is the factored form of the polynomial?

A polynomial has a leading coefficient of 1 and the following factors with multiplicity1 x2 i X V2 What is the factored form of the polynomial class=

Respuesta :

Answer:

(A)[tex][x-(2+i)][x-(2-i)][x-\sqrt{2}][x+\sqrt{2}][/tex]

Step-by-step explanation:

A polynomial has a leading coefficient of 1 and the  following factors with multiplicity 1:

[tex]x-(2+i)\\x-\sqrt{2}[/tex]

We apply the following to find the factored form of the polynomial.

  • If a complex number is a root of a polynomial with real coefficients, its complex conjugate is also a root of that polynomial.
  • If the polynomial has an irrational root [tex]a+\sqrt{b}[/tex], where a and b are rational and b is not a perfect square, then it has also a conjugate root [tex]a-\sqrt{b}[/tex].

[tex]\text{Complex conjugate of }x-(2+i)=x-(2-i)\\\\\text{Complex conjugate of }x-\sqrt{2}=x+\sqrt{2}[/tex]

Therefore, the factored form of the polynomial is:

[tex][x-(2+i)][x-(2-i)][x-\sqrt{2}][x+\sqrt{2}][/tex]

Answer:

A

Step-by-step explanation:

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