Algebra 2 Rational Root Theorem, Remainder Theorem, Factor Theorem, Descartes Rule of Signs and Fundamental Theorem of A

Is (x-4) a factor of (x³ +x² -16x-16)?

• YES

• NO

Find all the real zeros of the function 
f(x) = 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

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = 2x³ + 5x² - 9x + 5

• ±1, ±5, ±1/2, ±5/2

• ±1, ±2, ±5, ±1/2, ±5/2

• ±1, ±5

• ±1, ±2, ±5, ±1/2, ±5/2, ±2/5

Is (x-2) a factor of             f(x)= x³-8x²+14x-4?

• Yes, (x-2) is a factor. There is a remainder.

• No, (x-2) is  not a factor. The remainder is zero.

• Yes, (x-2) is a factor. The remainder is zero.

• No, (x-2) is  not a factor. There is a remainder. 

Which of the following statements is a direct consequence of the Fundamental Theorem of Algebra?

• Every polynomial of degree greater than zero has at least one real root.

• Every polynomial of degree greater than zero has at least one complex root.

• Every polynomial can be factored into linear factors in the set of real numbers.

• Every polynomial can be factored into linear factors in the set of complex numbers.

What does the Fundamental Theorem of Algebra state about the number of complex roots a polynomial equation has?

• At least one

• Exactly as many as its degree

• At most as many as its degree

• None of the above

• 1

• 3

• 5

• None of the above

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

• 4

• 5

• 6

• 7

What statement must be true about the this polynomial?

• It has exactly 3 roots (including repeated roots) and they have to be real numbers

• It has exactly 5 roots (including repeated roots) that may be real or complex numbers

• It has exactly 3 roots (including repeated roots) that may be real or complex numbers

• It has exactly 5 roots (including repeated roots) and they have to be real numbers

According to the Rational Root Theorem, what are the all possible rational roots? 
2x³ - 11x² + 12x + 9 = 0

• ±1,±2

• ±1,±3,±9

• ±1,±3±9,±1/2,±3/2,±9/2

• ±1,±2,±1/3,±2/3,±1/9,±2/9