Fundamental Theorem of Algebra

Fundamental Theorem of Algebra

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Multiple Choice

The degree of the polynomial determines the number of roots.

• True
• False

Multiple Choice

How many solutions does the polynomial f(x)=3x⁴ + 5x² - 6x have?

• 4
• 2
• 3
• 5

Multiple Choice

What is the total number of roots for the following equation?
y = 4x⁶ - 12x⁵ - x⁴ + 2x³ - 6x² - 5x + 10

• 4
• 5
• 6
• 7

Multiple Choice

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial. 

• A
• B
• C
• D

Multiple Choice

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial. 

• A
• B
• C
• D

Multiple Choice

All imaginary roots comes in pairs.

• True
• False

Multiple Choice

We Do:

A Polynomial of Degree 6 CAN have the following number of imaginary roots:

• 1

• 4

• 3

• 8

Multiple Choice

We Do:

A Polynomial of Degree 6 has 4 real roots, how many roots are imaginary roots?

• 2

• 4

• 3

• 8

Multiple Choice

You Do:

A Polynomial of Degree 9 CAN have the following number of imaginary roots:

• 1

• 10

• 3

• 8

Multiple Choice

You Do:

A Polynomial of Degree 9 has 5 real roots, how many roots are imaginary roots?

• 2

• 4

• 3

• 8

Multiple Choice

You Do: (Trick Question)

A Polynomial of Degree 3 has 2 real roots, how many roots are imaginary roots?

• 2

• 3

• 1

• Not possible

Multiple Choice

We Do:

Write x = -3 in its factored form

• (x - 3)

• (x + 3)

• (3x + 1)

• (3x - 1)

Multiple Choice

We Do:
 $x=\frac{1}{2}$ in factored form: 

• (2x + 1)

• (1x + 2)

• (2x - 1)

• (2x - 2)

Multiple Choice

We Do:

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ + 2x² - 11x - 12

• -3

• -4

• 1

• 6

Multiple Choice

You Do:

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ + 2x² - 11x - 12

• -3

• -4

• 1

• 6

Multiple Choice

We Do:

What are the three factors for

(x³ +7x² +7x -15) ÷ (x -1)?

• (x-1) (x+5) (x-3)

• (x-1) (x+5) (x + 3)

• (x+1) (x+5) (x-3)

• (x+1) (x-5) (x-3)

Multiple Choice

You Do:

What are the three factors for

(x³ -3x² -4x +12) ÷ (x + 2)?

• (x-2) (x+2) (x+3)

• (x-2) (x-2) (x+3)

• (x+2) (x+2) (x+3)

• (x-2) (x+2) (x-3)

Multiple Choice

We Do:

What are the zeros of the polynomial?

g(x) = 2x⁴ + 23x³ +19x² - 116x - 60

• 2,-3,-10,1/2

• 2, 3,-10,-1/2

• 2,-3,-10,-1/2

• -2,-3,10,-1/2

Multiple Choice

You Do:

What are the zeros of the polynomial?

h(x) = x⁴ + 3x³ - 55x² - 99x +630

• -5,6,-3,7

• 5 6, 3, -7

• -5, 6, 3, -7

• 6, 3, -7