Free Printable Fundamental Theorem of Algebra

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Fundamental Theorem of Algebra

Total questions: 13

Worksheet time: 1hrs 5mins

Name

Class

Date

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

Degree: 6

Degree: 5

Degree: 3

Degree: 2

How many zeros does the following function have?
f(x)= x⁵- 3x³ + x

The degree of the polynomial determines the number of roots.

True

False

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

Which of these is a possible root of the polynomials?
x³ - 6x² - x + 30

-9

-15

The Fundamental Theorem of Algebra tell us two things. Which of the options does not come from the Fundamental Theorem of Algebra?

A nth degree polynomial has at least 1 complex solution

An nth degree polynomial always has 2 x-intercepts

A nth degree polynomial has n solutions.

Find the zeros of the polynomial given one factor. Use synthetic division.

X= 3,4,5

x=-3,-4,-5

x=-3,4,5

x= 3, -4, -5

State how many of each type of possible solution the following polynomial has

f(x) = -4x⁴ + x³ +11x²- 4x + 8

Positive: 3 or 1

Negative: 1

Positive: 3

Negative: 1

Positive: 1

Negative: 3 or 1

Positive: 1

Negative: 3

10.

How many possible negatives solutions does the following polynomial have?

f(x) = x⁴ - 3x³ - 17x² + 39x -20

3 or 1

2 or 0

11.

The nth degree of a polynomial is equal to the number of root that same polynomial has: is a true statement of which theorem?

Factor Theorem

Remainder Theorem

Fundamental Theorem

All of the above

None of the above

12.

Which formula is the Fundamental Theorem of Algebra Formula?

There are infinitely many rationals between two reals.

Every polynomial equation having complex coefficents and degree greater than the number 1 has at least one complex root.

There are infinitely many prime numbers.

All numbers are rational numbers.

13.

Find all the real zeros of the function

y = 2x³ - 19x² + 38x + 24 given that (x-4) is a factor.

x = 1/2, -6

x = -1/2, 6

x = 4, -1/2, 6

x = -4, 1/2, -6

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Fundamental Theorem of Algebra

Total questions: 13

Worksheet time: 1hrs 5mins

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