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Writing Polynomial Functions from Complex Roots

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

Graph of f(x)

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

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

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

f(x) = x⁴ – 3x² – 4

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 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))

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

f(x) = -x² + 8x – 16

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

Graph of f(x)

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

Graph of f(x)

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

Graph of f(x)

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)

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

-6i

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