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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. 

 Nov 9, 2017
 #1
avatar+107156 
+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 !!!

 

 

cool cool cool

 Nov 9, 2017

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