AnswersINMT3 Integrated Math 3 Sem 1 26-27Writing Polynomial Functions from Complex Roots

Writing Polynomial Functions from Complex Roots Answers

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A polynomial function with a leading coefficient of 1 and multiplicity 1 for each factor has the following roots:x–2, x–(1+), x+3iAnother factor of the polynomial is:

Question illustration
A
x+2
Option A
B
x-(1-)
Option B
C
x-
Option C
2
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Which is the polynomial equation of lowest degree that has –10, –1, 3, and 4 as roots?

A
f(x) = (x – 10)(x – 1)(x + 3)(x + 4)
B
f(x) = x(x – 10)(x – 1)(x + 3)(x + 4)
C
f(x) = (x + 10)(x + 1)(x – 3)(x – 4)
D
f(x) = x(x + 10)(x + 1)(x – 3)(x – 4)
3

The complex conjugates theorem states that another factor of the polynomial is 3ixx + 2✔ x – 3i.

A
3ix
B
x + 2
C
✔ x – 3i
4

What is the degree of the polynomial?

Answer:

PENDING

5

Which of the following are factors of the polynomial?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
E
Option
Option E
F
Option
Option F
6

A polynomial function with a leading coefficient of 1 and multiplicity 1 for each factor has the following zeroes: How many total factors does the polynomial have? ⇒ 4

Question illustration
Answer:

PENDING

7

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

A
f(x) = (x – 2)(x – 5)
B
f(x) = x(x – 2)(x – 5)
C
f(x) =(x + 2)(x + 5)
D
f(x) = x(x + 2)(x + 5)
8

What is the factored form of the polynomial?

A
Option
Option A
B
Option
Option B
C
Option
Option C
9

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

A
f(x) = (x + 4)(x – 1)(x – 3)
B
f(x) = x(x + 4)(x – 1)(x – 3)
C
f(x) = (x – 12)(x + 4)(x – 1)(x – 3)
10

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?

A
x3 – 2x2 – 3x
B
x2 – 2x – 3
C
2x2 – 4x – 6
D
2x3 – 4x2 – 6x
11

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

A
x3 + x2 – 2x
B
2x3 + 2x2 – 4x
C
3x3 + 3x2 – 6x
D
–3x3 – 3x2 + 6x
12

What is the polynomial function?

A
f(x) = x4 + 3x2 – 10
B
f(x) = x4 – 4x3 + 5x2 – 2
C
f(x) = x4 – 4x3 + 3x2 + 8x – 10
13

The cubic function shown by the graph is

A
x3 – 13x + 12
B
2x3 – 26x + 24
C
x3 – 13x2 + 144x – 144

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