Higher Degree Polynomials

Question 1

What is the fundamental theorem of algebra?

Answer 1

The number of roots is equal to the degree of the polynomial.

Question 2

What are multiplicities?

Answer 2

The number of times a root exists.

Question 3

If a root’s multiplicity is odd what does that mean about the graph’s interaction with the x-axis?

Answer 3

It crosses the x-axis.

Question 4

If a root’s multiplicity is even what does that mean about the graph’s interaction with the x-axis?

Answer 4

It touches the x-axis, but does not cross it.

Question 5

Sum of cubes

Answer 5

a^3 + b^3 = (a + b)(a^2 – ab + b^2)

Question 6

Difference of cubes

Answer 6

a^3 – b^3 = (a – b)(a^2 + ab + b^2)

Question 7

How to find the number of possible roots?

Answer 7

If a real number, then p/q is a possible root where p is a divisor of the constant and q is a divisor of the leading coefficient (q ≠ 0). List all of the possible p’s over all of the possible q’s and don’t forget the ±.