Question

A polynomial has a leading coefficient of 1 and the

Answer 1

Answer:

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

Step-by-step explanation:

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

$x-(2+i)\\x-\sqrt{2}$

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 $a+\sqrt{b}$, where a and b are rational and b is not a perfect square, then it has also a conjugate root $a-\sqrt{b}$.

$\text{Complex conjugate of }x-(2+i)=x-(2-i)\\\\\text{Complex conjugate of }x-\sqrt{2}=x+\sqrt{2}$

Therefore, the factored form of the polynomial is:

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

Answer 2

Answer:C

Step-by-step explanation: