Polynomial Theorems

When (9x⁴- 45x³ + 37x² + x +2) is divided by (x-2), find the remainder.

• 656

• 652

• -64

• -368

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

• YES

• NO

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

• 2x³ - x² + x + 9

• 2x² - x + 1

• 2x² - x + 1 + 9/x-2

• 2x² - 9x - 15 - 23/x-2

(x – r) is a factor of P(x) if and only if __________.

• P(r) ≠ 0

• P(r) = 1

• P(r) = 0

• P(r) has two negative roots

Which of the following theorems allow us to use synthetic division to evaluate a polynomial at a given value?

• Fundamental Theorem of Algebra

• Remainder Theorem

• Factor Theorem

• Theorem of Polynomial Evaluation

Which of the following theorems tells us that if the degree of the polynomial is 3, then there are exactly three solutions to the polynomial?

• Fundamental Theorem of Algebra

• Remainder Theorem

• Factor Theorem

• Degree and Solutions Theorem

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

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

Use the Complex Conjugate Root Theorem to state another complex solution. Given that 3+5i is a root. 

• -3+5i

• -3-5i

• -5i

• 3-5i

Expand

• A

• B

• C

• D