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lozanna [386]
2 years ago
13

Which of the following polynomials has an even degree and a negative leading coefficient?

Mathematics
1 answer:
spin [16.1K]2 years ago
4 0

Using limits, the polynomial that has an even degree and a negative leading coefficient is:

Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0.

<h3>What is a limit?</h3>

A limit is given by the value of function f(x) as x tends to a value.

In this problem, to find the polynomial, we have to find the limits as x goes to infinity, hence:

\lim_{x \rightarrow -\infty} f(x) = [tex]\lim_{x \rightarrow -\infty} -a x^n

Since n is even, we have that:

  • \lim_{x \rightarrow -\infty} -a (-\infty)^n = -a \times \infty = -\infty
  • \lim_{x \rightarrow \infty} -a (\infty)^n = -a \times \infty = -\infty

Since it goes down to the left and down to the right, hence the function is:

Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0.

More can be learned about limits at brainly.com/question/26270080

#SPJ1

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