Question

the following info is known about a cubic polynomial function: p(-1)=0, p(3)= 0, p(6)=0 and p(5)=48. Find the equation of the function in factored form.

Answer 1

Since at x=1,3and 6 y=0 Our roots will be at 1,-3 and -6
p(x)=a(x+1)(x-3)(x-6)
Solve for a:
48=a(5+1)(5-3)(5-6)
Once you solve for a .... Voila you have your equation

Answer 2

I get it. Thank you soooo much! Can i ask you another question?

Answer 3

yes

Answer 4

What are the potential integral zeros of the polynomial p(x)=6x^3-2x^2-x+4?

Answer 5

Not sure what potential integral zeros mean

Answer 6

me either ;(

Answer 7

@bibby

Answer 8

idk google it nerd

Answer 9

I did a$$hole .

Answer 10

bby pls

Answer 11

i think it's something about the leading coefficient and constant term.

Answer 12

k gonna google it

Answer 13

Ohh found it :)

Answer 14

really?!

Answer 15

a= factors of constant term which is 4
a=1,2,4
b= factors of leading coefficient which is 6
b=1,2,3,6

Answer 16

what do i do with them?

Answer 17

Potential Integral Zeroes are +-a/b

Answer 18

So the potential integral zeroes would be 1, 1/2, 1/3, 1/6,2,2/3,4,4/3

Answer 19

1,2,4
1/2,1, 4/2
1/3,2/3,4/3
1/6,2/6,4/6

We can simplify it to ...
1,2,4, 1/2,1/3,2/3,4/3,1/6

Answer 20

thank you soooooo much for the help! :)

Answer 21

np

Answer 22

can I ask you another question if you don't mind? I have a test tomorrow.

Answer 23

ya sure

Answer 24

i posted the question.

Answer 25

"potential integral zeros of the polynomial"
INTEGRAL zeros means zeros that are INTEGERS.
6x^3-2x^2-x+4
For potential integer zeros you need to consider only the factors of the constant term. Here the constant term is 4. And the factors of 4 are: 1, 2 and 4.
The potential integral zeros are: 1, 2 and 4.

There is another theorem called the rational roots theorem where you consider the factors of the constant term divided by the factors of the leading coefficient. But that is not what they are asking here.