Polynomial Theorems

When p(x) = 9x⁴- 45x³ + 37x² + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?

• p(2) = 656

• p(2) = 652

• p(2) = -64

• p(2) = -368

If dividing polynomial g(x) by (x – 1) yields a remainder of 2, which must be true?

• g(1) = 2

• g(-1) = 2

• g(2) = 1

• g(2) = -1

What is the remainder when a³ - 4 is divided by a+2? 

• -2

• -6

• -12

• 0

What are the three factors for
 (x³ -3x² -4x +12) ÷ (x + 2)?

• (x-2) (x+2) (x+3) 

• (x-2) (x-2) (x+3)

• (x+2) (x+2) (x+3)

• (x-2) (x+2) (x-3)

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

If a polynomial has 2 factors, it will have 2 zeros (or 1 zero with a multiplicity of 2).

• True

• False

What is the Fundamental Theorem of Algebra?

• The degree of the polynomial determines what the x value will be

• The degree of the polynomial tells us how many solutions the polynomial will have.

• States that a complex number and its conjugate are solutions

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

• 4

• 5

• 6

• 7

A polynomial of degree n has

• only 1 zero

• exactly n zeroes

• at most n zeroes

• more than n zeroes