Where did the 5x+6 come from?

Question

I got an equation, (x^3+5x+6)/6, to a table. The x numbers are 0, 1, 2, 3, 4, 5 and the y numbers are 1, 2, 4, 8, 15, 26. I got this equation by help but i don't understand how it's the equation to the table i made. The question that was asked to me was "into how many parts will five random planes divide space?" i don't understand where the 5x+6 came from! I need help!

Answer 1

the equation is y=(x^3+5x+6)/6
and the ordered pairs are
(0,1)(1,2)(2,4)(3,8)(4,15)(5,26)
since it is a third degree equation the genera form is
f(x)=ax^3+bx^2+cx+d
f(1)=a+b+c+d...........=1....(1)
f(2)=8a+4b+2c+d.....=2...(2)
f(3)=27a+9b+3c+d...=4...(3)
f(4)=64a+16b+4c+d.=8....(4)
if you solve you will get a=1/6,b=0,c=1
giving the equation as (1/6)x^3+(5/6)x+1

Answer 2

If they are random planes, placed in space randomly you would have to have a number between 2 and the max number.

Each new plane can only cross over the amount of planes already in space.


2 = 4
3 = 7
4 = 11
5 = 15

It looks like above 7 planes, 4 divides are added each time.

Answer 3

your equation does not have the y variable in it. Did you type it out correctly when you wrote this post? Check the equation again, it must have both the x and the y variables. Make a repost and I'll look for it and try to help you out.

Answer 4

You substitute each x into the function, do the math and get the corresponding y