+0  
 
0
45
1
avatar

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
Sort: 

1+0 Answers

 #1
avatar+78762 
+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

CPhill  Nov 9, 2017

7 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details