Question

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots?

A ) f(x) = (x - 1)(x + 1)^11

B ) f(x) = (x + 2)^3(x^2 -7x +3)^4

C ) f(x) = (x^5 + 7x + 14)^6

D ) f(x) = 11x^5 + 5x + 25


I originally chose A, but that was incorrect on my quiz.

Answer 1

The correct answer is B

Explanation:

Answer 2

B would be the right one

F(x) = (x+2)^3 = the highest power for this type turn out will be x^3
the other part is (x^2 - 7x + 3)^4, the highest power for this part will be x^8
since (x+2)^3(x^2-7x +3)^4 = the highest power of first part x^3 second part x^8
x^3 * x^8 = x^11 that result in 11 roots
This type of math, you don't need to configure the whole problem, you just need to know the basic rules of power of a number. For example, (x^2)^3, then 2*3 = 6 make x^6.
or x^2 * x^3 = x^2 + 3 = x^5.