Answers Common Core Algebra II A-ICWriting Polynomial Functions from Complex Roots

Writing Polynomial Functions from Complex Roots Answers

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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)

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

x – 3

x – 1

x + 1

x + 3

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))

Which polynomial function could be represented by the graph below?

f(x) = x2 – 6x + 8

f(x) = 3x2 – 18x + 24

f(x) = x2 + 6x + 8

f(x) = 3x2 + 18x + 24

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)

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

x – 3

x – 1

x + 1

x + 3

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