Writing Polynomial Functions from Complex Roots

If a polynomial function f(x) has roots 4 - 13i and 5, what must be a factor of f(x)?

(x - (4 + 13i))

If a polynomial function f(x) has roots 0, 4, and , what must also be a root of f(x)?

3 - squrt11

Which polynomial function f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity 1, and root -5 with multiplicity 3?

f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x - 2)(x - 9)

Which second degree polynomial function has a leading coefficient of -1 and root 4 with multiplicity 2?

f(x) = -x2 + 8x - 16

Which polynomial function has a leading coefficient of 3 and roots -4, i, and 2, all with multiplicity 1?

f(x) = 3(x + 4)(x - i)(x + i)(x - 2)

Which polynomial function could be represented by the graph below?

f(x) = 3x2 - 18x + 24

What is the polynomial function of lowest degree with lead coefficient 1 and roots i, -2, and 2?

f(x) = x4 - 3x2 - 4

What must be a factor of the polynomial function f(x) graphed on the coordinate plane below? swoop left

x+6

What must be a factor of the polynomial function f(x) graphed on the coordinate plane below? right swoosh

x-3

If a polynomial function f(x) has roots 3 and , what must also be a root of f(x)?

- squrt 7