Algebra 2 // Writing Polynomial Functions from Complex Roots

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

x - 3

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 -9 and 7 - i, what must be a factor of f(x)?

(x - (7 + i))

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

C

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

NOT f(x) = -x2 + 8x + 16

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

NOT f(x) = x4 + 3x2 - 4, f(x) = x4 - 3x2 - 4

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

NOT A

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

NOT B, A

Which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 - i) with multiplicity 1?

NOT f(x) = (x + (7 - i))(x + (5 + i))(x + (7 + i))(x + (5 - i))