# A polynomial has a leading coefficient of 1 and the following factors with multiplicity 1: x- (2+i) x-√2 W

A polynomial has a leading coefficient of 1 and the
following factors with multiplicity 1:
x- (2+i)
x-√2
What is the factored form of the polynomial?
O
[x-(2+i)][x-(2-i)](x-√2)(x+√2)
O [x-(2+i)][x+(2-1)](x-√√2)(x+√2)
[x-(2+i)][x+(2+i)](x-√2)(x+√2)

### 1 thought on “A polynomial has a leading coefficient of 1 and the following factors with multiplicity 1: x- (2+i) x-√2 W”

1. The factored form of the polynomial is:
=> [x-(2+i)][x-(2-i)](x-√2)(x+√2)
Given:
In the question:
A polynomial has a leading coefficient of 1 and the following factors with multiplicity 1:
x- (2+i)
x-√2
To find the factored form of the polynomial?
Now, According to the question:
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 +√b  , where a and b are rational and b is not a perfect square, then it has also a conjugate root a – √b.
Complex Conjugate of x- (2+i) = x – (2 – i)
Complex Conjugate of x-√2 = x + √2
Therefore, the factored form of the polynomial is:
=> [x-(2+i)][x-(2-i)](x-√2)(x+√2)