Question

Is the value of the constant term for the function: h(x)=4x^4-5x^3+2x^2-x+5, 5 ? If so, how do I find all of the factors of the constant term?

Answer 1

Would the factors be 1 and 5 ?

Answer 2

yes, and yes

Answer 3

although the integer factors could also be \(-1\) and \(-5\)

Answer 4

is this topic "rational root theorem"?

Answer 5

so should I put ±1, ±5 ?

Answer 6

for possible rational roots, yes

Answer 7

It's "Polynomial and Rational Functions"

Answer 8

how'd i guess?

Answer 9

you're amazing, that's how :p

Answer 10

(blush)

Answer 11

hehe, would the leading coefficient be -5 with the factors ±1, ±5 also?

Answer 12

oh no, the leading coefficient would be 4, right? with the factors 1 and 4?

Answer 13

No! The possible rational roots are: +-1, +-5, +-1/2, +-5/2, +-1/4, +-5/4

Answer 14

Because the factors of the leading coefficient, 4, are 1,2 and 4

Answer 15

oh okay, but in the list you put of possible rational roots, how did you get ±5, ±5/2, and ±5/4? where did the 5 come from?

Answer 16

good point you need fractions of the form \(\frac{p}{q}\) were \(p\) divides \(5\) and \(q\) divides \(4\)

Answer 17

Every possible rational roots has to be of the form p/q where p is a factor of the constant term and q is a factor of the leading coefficient

Answer 18

where is the 5 coming from though? I don't understand that part at all, the rest I do

Answer 19

so the denominators can be \(1, 2\) or \(5\)

Answer 20

oh okay!

Answer 21

well that was a typo
denominators can be 1, 2 or 4

Answer 22

gotcha! so the possible rational roots are only +-1, +-5, +-1/2, +-5/2, +-1/4, +-5/4?