Polynomials

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

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

• 5

• 4

• 3

• 2

Give the correct name for
-3x⁴-3x²+5

• Constant Trinomial

• Quartic Trinomial

• quadratic Trinomial

• Linear Trinomial

Give the correct name for 
2x³+5x

• Linear Binomial

• Cubic Binomial

• Quadratic Trinomial

• Linear Trinomial

• (-2.55, 0), (2.55, 0)
• (-3, 0), (-2, 0), (2, 0), (3, 0)
• (0, 36)
• (0, -3), (0, -2), (0, 2), (0, 3)

What is the end-behavior?

• lim x-> -oo    f(x) -> oo
   lim x-> oo     f(x) -> -oo

• lim x-> -oo    f(x) -> oo
   lim x-> oo     f(x) -> oo

• lim x-> -oo    f(x) -> -oo
   lim x-> oo     f(x) -> oo

• lim x-> -oo    f(x) -> -oo
   lim x-> oo     f(x) -> -oo

Is it possible for a quartic polynomial to have 0 real solutions?

• Yes

• No

Write a polynomial of least degree that has real coefficients and a leading coefficient of 1 with the zeroes 8 and i.

• x³ - 7x² + 14x - 8

• x³ - 8x² + x - 8

• x² + x - 8

• x³ + 8x² - x + 8

Imagine Mason is analyzing a polynomial function f(x) = x^4 - 12x + 1 as part of his mathematics project. Including all real and imaginary solutions, how many solutions exist for this function?

• 0

• 1

• 2

• 4

During a mathematics competition, Priya is tasked with analyzing the polynomial (x^8 + 2x^5 - x^4 + 6). Which statement is true about this polynomial?

• It has exactly 4 roots, including any repeated roots, that must be real numbers.

• It has exactly 8 roots, including any repeated roots, that must be real numbers.

• It has exactly 4 roots, including any repeated roots, that may be either real or complex numbers.

• It has exactly 8 roots, including any repeated roots, that may be either real or complex numbers.