464,672 views
12 votes
12 votes
What is the behavior of the graph y = -x6 - 6x5 + 50x³ +45x² - 108x-108 at each of its zeros?

What is the behavior of the graph y = -x6 - 6x5 + 50x³ +45x² - 108x-108 at each of-example-1
User Mockee
by
3.2k points

1 Answer

19 votes
19 votes

We have to find the behaviour of the polynomial at each of its zeros.

To find that we need to factorize the polynomial.

There is no direct way to factorize a sixth degree polynomial. We will use a graph of the function:

We can then see that the zero at x = -3 behaves as a cubic polynomial, the zero at x = -1 behaves linearly and x = 2 behaves as a quadratic polynomial.

Each zero will probably have the corresponding multiplicity (the cubic polynomial behaviour correspond to a zero with multiplicity of 3).

Answer: one resembles a cubic function, one resembles a linear function and one resembles a quadratic function.

What is the behavior of the graph y = -x6 - 6x5 + 50x³ +45x² - 108x-108 at each of-example-1
User Achmed
by
2.3k points