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))
