Polynomial Theorems

The degree of the polynomial determines the number of solutions (roots).

Example: All cubic polynomials have exactly 3 solutions.

• True

• False

Given that 3+5i is a solution to a given polynomial, determine another solution that the polynomial must have.

• -3+5i

• -3-5i

• -5i

• 3-5i

To determine if one polynomial is a factor of the other, use synthetic division to see if the remainder is...?

• -1

• 0

• 1

• the same as the number you are dividing by.

Use synthetic substitution to find f(2) for f(x) = x³ - 5x² + 8x + 10.

• -34

• 14

• 38

• 6

How many solutions does the following function have? f(x)= x⁵ - 3x³ + x

• 8

• 9

• 5

• 3

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

Which of these are possible combinations for the types of solutions of the given polynomial: [Select 3 answers] Remember that imaginary solutions always come in pairs. 4x^5+8x^2-18x+11

• 5 real (no imaginary)

• 3 real and 2 imaginary

• 1 real and 4 imaginary

• 0 real and 5 imaginary

• 2 real and 3 imaginary

Paul divided a polynomial by x-3 and the remainder was 7. What does this tell Paul?

• The polynomial does not have a solution at x = 3.

• The polynomial does not have a solution at x = -3.

• The polynomial has a solution at x = -3.

• The polynomial has a solution at x = 3.

Paul performed synthetic division on a polynomial with the value 3 the remainder was 0. What does this tell Paul?

• The polynomial does not have a solution at x = 3.

• The polynomial has a solution at x = 3.