Polynomial Functions and Number of Real Zeros

Which of the following is a 5th degree trinomial with a leading coefficient of -2? 

• -2x⁵ + 3x - 1
• 5x^-2 +3x - 1
• -2x⁵ + 3x⁴ + 2x³ + x² - 10
• 2x + 5

List all possible rational zeros

f(x) = 3x⁵ - 5x² + x + 6

• 1, 2, 3, 6, -1, -2, -3, -6

• 1/3, 2/3, 1, 2, 3, 6, -1/3, -2/3, -1, -2, -3, -6

• 1/3, 2/3, 1, 2, 3, 6

Tags

CCSS.HSA.APR.B.2

What is the degree of the polynomial function

P(x)=3x⁴ - 7x² - 2x⁷ - x + 4?

• 4

• 7

• 2

• 1

The polynomial
f(x) = 5x⁴ + 2x³ + 2x − 7 can have, at most, how many solutions?

• 5
• 4
• 3
• 2

• 2
• 1
• 4
• None

Tags

CCSS.HSA.APR.B.3

State the possible number of positive real zeros, negative real zeros, and imaginary zeros of the function f(x)=-4x⁴-2x³-12x²-x-23. 

• 0 positive
  4 or 2 negative
  0 or 4 imaginary
• 0 positive
  4,2, or 0 negative
  4, 2, or 0 imaginary
• 0 positive
  1 negative
  3 imaginary
• 2 or 0 positive
  2 or 0 negative
  4, 2, or 0 imaginary

State the number of REAL ZEROS for the function:

f(x) = 2x⁴ + 19x² + 24

• 4, 2, 0

• 4, 2

• 0

• 4

State the possible number of IMAGINARY ZEROS for the function:

f(x) = 2x⁴ + 19x² + 24

• 4, 2, 0

• 4, 0

• 0

• 4

A polynomial function with rational coefficients of degree 4 MUST have at least 1 real zero.

• True

• False

A polynomial function with rational coefficients of degree 3 MUST have at least 1 real zero.

• True

• False