Question

List the potential rational zeros of the following function. x^3+5x^2-12x+14 = 0

Please explain.
@Calculus1

Answer 1

The potential rational zeros are of the form p/q where p is a factor of the last coefficient and q is a factor of the first coefficient


So the potential zeros are: 14/1, -14/1, 7/1, -7/1, 2/1, -2/1, 1/1, -1/1


which reduce to: 14, -14, 7, -7, 2, -2, 1, -1

Answer 2

How did you get this answer? Im just curious so I will know how to do it

Answer 3

I divided the possible factors of 14 (the last coefficient/term) by the possible factors of 1 (the first coefficient)


The factors of 14 are: 14, 7, 2, 1, -1, -2, -7, -14

and the factors of 1 are: 1, -1

Answer 4

Notice how the factors come in plus/minus pairs

Answer 5

ohh ok. thank you. :)

Answer 6

so if you write out the division, what do you get? (when you divided by 14)

Answer 7

Dividing all the terms gives us the possible rational zeros of: 1, -1, 2, -2, 7, -7, 14, -14

Note: I sorted the terms

Answer 8

yeah but what does the function look like when you are dividing?

Answer 9

I'm not working with the function, just the factors of the first and last coefficients

Answer 10

ohhh- duh...ok i got it now that you say that. LOL!! Thank you, I feel so dumb when it comes to this stuff.

Answer 11

np, don't worry about it, it just takes practice

Answer 12

I agree to that. lol

Answer 13

so no need to worry about feeling dumb, it'll all come easier in time