Writing Polynomial Functions from Complex Roots Assignment Study Guide

A polynomial function with a leading coefficient of 1 and multiplicity 1 for each factor has the following roots: x-2 x-(1+ √5 x+3i) Another factor of the polynomial is:

x-(1-√5)

Which of the following are factors of the polynomial?

x-2√11 x+2√11 x-(1-i) x-(1+i)

The complex conjugates theorem states that another factor of the polynomial is

x-3i

The cubic function shown by the graph is

x³ - 13x + 12

A polynomial has x-intercepts of 3, 0, and -1, and passes through the point (1, -8). Which of the following functions could represent this graph?

2x³ - 4x² - 6x

Which of the following polynomial functions could represent the graph on the right?

3x³ + 3x² - 6x

A polynomial function with a leading coefficient of 1 and multiplicity 1 for each factor has the following zeroes: -2√11 1-i How many total factors does the polynomial have?

4

What is the degree of the polynomial?

5

Which of the following items did you include in your response?

Select all

What information must you have to write a polynomial function having all real roots given its graph?

The x-intercepts of the graph, or the zeroes of the function. The multiplicity of its factors. A point on the graph that is not a root, or the value of the leading coefficient.

A polynomial has a leading coefficient of 1 and the following factors with multiplicity 1: x − (2 + i) x − √2 What is the factored form of the polynomial?

[x-(2+i)][x-(2-i)](x-√2)(x+√2)

Which is the polynomial equation of lowest degree that has -10, -1, 3, and 4 as roots?

f(x) = (x + 10)(x + 1)(x - 3)(x - 4)

Which of the following could represent the function shown in the graph?

f(x) = (x + 4)(x - 1)(x - 3)

Which is the polynomial function of lowest degree that has -5, -2, and 0 as roots?

f(x) = x(x + 2)(x + 5)

What is the polynomial function?

f(x) = x⁴ - 4x³ + 3x² + 8x - 10