OpenStudy (anonymous):

Can someone please show me how to use the Rational Root Theorem and the Fundamental Theorem of Algebra to prove my function f(x)=x³+3x²-22x-24 matches my graph.

3 years ago
OpenStudy (anonymous):

here is the graph

3 years ago
OpenStudy (anonymous):

@phi @jdoe0001

3 years ago
OpenStudy (phi):

what is the rational root theorem ?

3 years ago
OpenStudy (phi):

that says that your rational roots would be one of the factors of 24 list the factors of 24

3 years ago
OpenStudy (phi):

then try each factor... use synthetic division (or polynomial division) to see if that factor is a zero. if it is, then you will get a quadratic that you can factor using the quadratic formula to find the other 2 roots. Fundamental Theorem of Algebra says that a polynomial of order 3 (highest exponent is 3) has exactly 3 roots.

3 years ago
OpenStudy (anonymous):

|dw:1389044077360:dw| So based on the rational root theorem, we know that the only possible roots are -1,1, ... , -24, 24 And based on the Fundamental Theorem of Algebra, we know that degree of the function is 3 because x^3 is the highest polynomial and thus there are 3 linear factors possible, hence 3 roots on the graph. The three roots on the graph, namely x = {4, -1, -6} corresponds to all the possible roots outlined in my drawing. So the function matches the graph in that aspect.

3 years ago