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))

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)

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

f(x) = x⁴ - 3x² - 4

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

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

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)

If a polynomial function f(x) has roots 0, 4, and 3+√11, what must also be a root of f(x)?

3 -√11

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

(x - (7 + i))

If a polynomial function f(x) has roots -8, 1, and 6i, what must also be a root of f(x)?

-6i

A factor of the polynomial function f(x) shown in the graph is (x - 1).

Graph of f(x)

A factor of the polynomial function f(x) shown on the graph is (x + 6)

Graph of f(x)

This polynomial function f(x) = -2x³ - 2x² + 12x could be represented by the graph.

Graph of f(x)

This polynomial function f(x) = 3x² - 18x + 24 could be represented by the graph.

Graph of f(x)