CW: Rational Root Theorem

Which of the following is a COMPLETE list of all possible Rational Zeros?

f(x) = x³ + 2x² - 6x + 8

• ±1, ±8

• ±1, ±2, ±4, ±8

• ±1, ±2, ±4

• 1, 2, 4, 8

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

• Degree: 6
• Degree: 5
• Degree: 3
• Degree: 2

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

True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing.

• True
• False, because the solution and root are the same but the x-intercept and zero are different
• False, because the x-intercept and root are the same but the zero and solution are different
• False, they are all different

Identify the missing term to complete the solution.

• 28

• 38

• 48

• 58

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

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

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

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

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

• p = -1, 1, -2, 2, -3, 3,

Give P(x) = -4x² + 3x³ - 17x + 6

As all possible zeroes = p/q =  $\pm$ {factor of constant/factor of leading coefficient}

• All possible zeroes =

   $\pm$ {1, 2, 3, 6, 1/1, 1/4, 2/1, 2/4, 3/1, 3/2, 3/4, 6/1, 6/2, 6/4}

• All possible zeroes =

   $\pm$  {1, 2, 3, 6,1/3, 2/3}

• All possible zeroes =

   $\pm$ {1, 2, 4, 1/2, 1/3, 1/6, 2/3, 4/3}

• All possible zeroes =

   $\pm$ {1, 2, 4, 1/2, 1/3, 1/6, 2/1, 2/2, 2/3, 2/6, 4/1, 4/2, 4/3, 4/6}

Find all the p/q factors for:
 $f\left(x\right)=2x^4-3x^3+5x+25$  

•  $\pm1,5,25,\frac{1}{2},\frac{5}{2},\frac{25}{2}$  

•  $\pm1,2,\frac{1}{5},\frac{2}{5},\frac{1}{25},\frac{2}{25}$  

•  $\pm1,5,25$  

•  $\pm1,2$  

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

• ±1, ±7, ±1/3, ±7/3
• ±1, 7
• ±1, ±3, ±7, ±7/3
• ±1, ±3, ±7, ±1/3, ±7/3