Hello, I heard about this site from a friend and I just really need urgent help on these two problems. If you can help that would be great, thanks in advance!

1. The table shows ordered pairs for a polynomial function f.

Heres the data in the table.

x=-3, -2, -1, 0, 1, 2, 3,

f(x)=63, 8, -1, 0, -1, 8, 63

Heres the question: What is the degree of f?

I've played around with this question and I found 21 to be a factor and also 4 (somehow), but I have no idea if I'm right because neither one works for all of the data shown. So yeah, I need help.

2. It says Alek is using synthetic division to divide x^3 + 4x^2 -43x -10 by x-5.

(I spreaded it out so that it could be easier to see)

On this question my answer is 5; 1 4 -43 -10

5 45 10

________________

1 9 2 0

(Long-Synthetic Division)

But once again, I'm not certain

Please help me, again I'm sorry I'm asking but I'm stuck.

Guest Nov 9, 2017

#1**+2 **

x= -3, -2, -1, 0, 1, 2, 3,

f(x)=63, 8, -1, 0, -1, 8, 63

Notice that when the graph progresses from (- 2, 8) to (-1, -1)...it passes through the x axis for the first time....so this is one zero

And then (-1, -1) to (0,0) ......given the fact that we're not told that graph reaches a posiitive value before it progresses to (1, -1)....we have to assume that it only "touches" the origin....this means that, -- at a minimum- two more "zeroes" are added

And from (-1, -1) to (2,8) it passes through the x axis once more....and a last zero is added

So...at a minimum, the graph has a degree of 4 [ the fact that the graph just "kissses" the origin means that the actual degree could also be 6, 8, 10, etc. When a graph just touches the x axis, it means that 2n zeroes are added.......

Your second one is correct !!!

CPhill
Nov 9, 2017