# Writing Polynomial Functions From Complex Roots

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question
Which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 - i) with multiplicity 1? f(x) = (x + 7)(x - i)(x + 5)(x + i) f(x) = (x - 7)(x - i)(x - 5)(x + i) f(x) = (x - (7 - i))(x - (5 + i))(x - (7 + i))(x - (5 - i)) f(x) = (x + (7 - i))(x + (5 + i))(x + (7 + i))(x + (5 - i))
C) f(x) = (x - (7 - i))(x - (5 + i))(x - (7 + i))(x - (5 - i))
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If a polynomial function f(x) has roots -8, 1, and 6i, what must also be a root of f(x)? -6 -6i 6 - i 6
B) -6i
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If a polynomial function f(x) has roots 4 - 13i and 5, what must be a factor of f(x)? (x + (13 - 4i)) (x - (13 + 4i)) (x + (4 + 13i)) (x - (4 + 13i))
Not, B) (x - (13 + 4i))
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What must be a factor of the polynomial function f(x) graphed on the coordinate plane below? mc017-1.jpg x - 3 x - 1 x + 1 x + 3
B) x - 1
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If a polynomial function f(x) has roots -9 and 7 - i, what must be a factor of f(x)? (x - (7 + i)) (x - (-7 - i)) (x + (7 + i)) (x + (7 - i))
Not, C) (x + (7 + i))
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Which polynomial function has a leading coefficient of 1 and roots 2i and 3i with multiplicity 1? f(x) = (x - 2i)(x - 3i) f(x) = (x + 2i)(x + 3i) f(x) = (x - 2)(x - 3)(x - 2i)(x - 3i) f(x) = (x + 2i)(x + 3i)(x - 2i)(x - 3i)
D) f(x) = (x + 2i)(x + 3i)(x - 2i)(x - 3i)
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If a polynomial function f(x) has roots 3 and mc001-1.jpg, what must also be a root of f(x)? mc001-2.jpg mc001-3.jpg -3 3i
A) mc001-2.jpg) -root7
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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) = 3(x + 5)(x + 4)(x - 2)(x - 9) f(x) = 3(x - 5)(x - 4)(x + 2)(x + 9) f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x - 2)(x - 9) f(x) = (x - 5)(x - 5)(x - 5)(x - 4)(x + 2)(x + 9)
C) f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x - 2)(x - 9)
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What must be a factor of the polynomial function f(x) graphed on the coordinate plane below? mc016-1.jpg x - 3 x - 1 x + 1 x + 3
Not, D) x + 3
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Which second degree polynomial function has a leading coefficient of -1 and root 4 with multiplicity 2? f(x) = -x2 - 8x - 16 f(x) = -x2 + 8x - 16 f(x) = -x2 - 8x + 16 f(x) = -x2 + 8x + 16
B)f(x) = -x2 + 8x - 16
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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 - 2) f(x) = (x - 3)(x + 4)(x - i)(x - 2) f(x) = (x - 3)(x + 4)(x - i)(x + i)(x - 2) f(x) = 3(x + 4)(x - i)(x + i)(x - 2)