Answers MVP MSD Common Core Algebra II A - MA3111 ICWriting Polynomial Functions from Complex Roots

Writing Polynomial Functions from Complex Roots Answers

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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

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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)

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

f(x) = x3 – x2 – 4x + 4

f(x) = x4 – 3x2 – 4

f(x) = x4 + 3x2 – 4

f(x) = x3 + x2 – 4x – 4

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))

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

Which polynomial function could be represented by the graph below?

f(x) = x3 + x2 – 6x

f(x) = x3 – x2 – 6x

f(x) = –2x3 – 2x2 + 12x

f(x) = –2x3 + 2x2 + 12x

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 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)

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))

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))

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

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Writing Polynomial Functions from Complex Roots Answers

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