if a polynomial function f(x) has roots -9 and 7 - i, what must be a factor of f(x)?\n(x - (7 + i))\n(x…

if a polynomial function f(x) has roots -9 and 7 - i, what must be a factor of f(x)?\n(x - (7 + i))\n(x - (-7 - i))\n(x + (7 + i))\n(x + (7 - i))

if a polynomial function f(x) has roots -9 and 7 - i, what must be a factor of f(x)?\n(x - (7 + i))\n(x - (-7 - i))\n(x + (7 + i))\n(x + (7 - i))

Answer

Explanation:

Step1: Recall root - factor relationship

If (r) is a root of a polynomial function (f(x)), then ((x - r)) is a factor of (f(x)).

Step2: Identify the factor for the complex root

Given a root (r = 7 - i), the corresponding factor is ((x-(7 - i))=(x - 7 + i)). Also, for a polynomial with real - valued coefficients, if (a+bi) is a root, then its complex conjugate (a - bi) is also a root. The complex conjugate of (7 - i) is (7 + i), and the factor corresponding to the root (7 + i) is ((x-(7 + i))).

Answer:

A. ((x-(7 + i)))