Question

Using the Fundamental Theorem of Algebra determine how many possible zeros there are for each polynomial function.

x^5-2x+1
2. 2x+5
3. (x-5)(x+2)

Answer 1

the fundamental theorem of calculus tells us a polynomial of degree \(n\) can have at most \(n\) real zeros

Answer 2

here are my answer choices
a. 2 Possible zeros
b. 5 Possible zeros
c. 3 Possible zeros
d. 1 Possible zero
e. 4 Possible zeros

Answer 3

wait so would the first one be 5

Answer 4

it's to the 5th degree

Answer 5

@oldrin.bataku maybe?

Answer 6

@sarahjones667 exactly! the first is 5th degree because the most significant term in the long run is \(x^5\) hence we have \(5\) possible zeros

Answer 7

so the 2nd and third would have 1 right?

Answer 8

the second would indeed have one but the third... well, count the number of zeros that are actually there since it's in factored form :-p

Answer 9

two!

Answer 10

one more. I'm confused by this one, do I take the biggest one? x^4-3x^2+5x-2

Answer 11

@oldrin.bataku sorry last question

Answer 12

@sarahjones667 good job! the third was indeed two :-) anyways, yes, the degree is determined by the biggest power of our variable -- in this case \(x^4\).

Answer 13

haha okay. thanks so much