Answers Summer_Advanced AlgebraWriting Polynomial Functions from Complex Roots

Writing Polynomial Functions from Complex Roots Answers

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Use substitution to write an equivalent quadratic equation.(3x + 2)2 + 7(3x + 2) – 8 = 0

u² + 7u - 8 = 0, where u = (3x + 2)²

u² + 7u - 8 = 0, where u = 3x + 2

u² + 7u - 8 = 0, where u = 7(3x + 2)

u² + u - 8 = 0

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Which equation is equivalent tof(x) = 16x4 – 81 = 0?

(4x² - 9)(4x² - 9) = 0

(4x² + 9)(4x² - 9) = 0

(4x - 9)(4x - 9) = 0

(4x + 9)(4x - 9) = 0

Solve x4 – 17x2 + 16 = 0.Let u = .

17x²

x²

-17x²

Rewrite the equation in terms of u.

u² - 17u - 16 = 0

17u² + u + 16 = 0

-u² + 17u + 16 = 0

u² - 17u + 16 = 0

Factor.

(u + 16)(u + 1) = 0

(u - 16)(u - 1) = 0

(u + 17)(u - 1) = 0

Solve (x + 3)2 + (x + 3) – 2 = 0.Let u =

x + 3

(x + 3)²

x²

Rewrite the equation in terms of u.

(u2 + 3) + u – 2 = 0

u2 + u – 2 = 0

(u2 + 9) + u – 2 = 0

u2 + u + 1 = 0

Factor the equation.

(u + 2)(u – 1) = 0

(u + 1)(u – 2) = 0

(u – 2)(u – 1) = 0

What are the solutions of 4x4 – 4x2 = 8?

x = ± i

x = ±1

Option

Solve the equation 6(2x + 4)2 = (2x + 4) + 2.

Option

Solve (x + 4)2 – 3(x + 4) – 3 = 0 using substitution.u =

x + 4

3(x + 4)

(x + 4)²

Select all of the solutions to the original equation.

x = 4

x = - 16

x = - 4

x = 16

x = - 8

x = - 1

x = 1

x = 8

What are the solutions of the original equation?

= 1 or x = –2

= –1 or x = 2

x = –5 or x = –2

= 4 or x = –5

Select the solution(s) of the original equation.

Option

Examine the criteria below. Check which of these you included in your response.

The equation is not quadratic in form.

The variable part of the first term is not the square of the variable part of thesecond term.

The result of squaring x cubed is x to the 6th power, not the 9th power.

x9 (x3)2

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Writing Polynomial Functions from Complex Roots Answers

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