Algebra Amazing Race Polynomials

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

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

• 4

• 2

• 3

• 5

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.

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

• A

• B

• C

• D

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

• 4

• 3

• 2

• 5

(x - 2) and (x - 4 ) are
the linear factors of x² - 6x + 8

• True

• False

• is the graph of
  y = x² - 2x + 4
• is the graph of
  y = -x² - 2x + 4

• Graph for odd polynomials (x³,x⁵,...)
• Graph for even polynomials (x²,x⁴,...)

As x goes to positive ∞, y goes to positive ∞ 
As x goes to negative ∞, y goes to negative ∞ As x goes to positive ∞, y goes to negative ∞ 
As x goes to negative ∞, y goes to positive ∞

• As x goes to positive ∞, y goes to positive ∞ 
  As x goes to negative ∞, y goes to negative ∞

• As x goes to positive ∞, y goes to negative ∞ 
  As x goes to negative ∞, y goes to positive ∞

Which problem can you use synthetic division?

• (x² + 20x + 16 ) ∕  (x² + 4)

• (x² + 20x + 16) ∕ (x + 4)

• Both problems

• None of these