Question

A. Find the remainder when 6x^1000 - 17x^562 + 12x +26 is divided by x+1.

B. Is x-1 a factor of x^567 - 3x^400 + x^9 +2?


I just need to see that the answer I have is correct :) thanks

Answer 1

Tell me what you got as remainder??

Answer 2

a. I got 27 using synthetic division.

Answer 3

Well I am not quite sure..

In B part,

to check x - 1 is the factor :

Put x = 1 in the given expression and tell me after solving does it become 0 or not?

Answer 4

I have told you..

If (x-1) is the factor then it must satisfy the given expression..

Plug in x = 1 in the given expression and check whether you get 0 or something else..

Answer 5

For a, are you sure you would like to use synthetic division? You'll have to write 998 '0's for that...

Answer 6

*997

Answer 7

okay, then tell me another way, i'm obviously learning here.

Answer 8

Use remainder theorem...
Let f(x) = 6x^1000 - 17x^562 + 12x +26
Since it is divided by x+1
remainder = f(-1) = 6(-1)^1000 - 17(-1)^562 + 12(-1) +26 =...

Answer 9

okay thankyou

Answer 10

Welcome. You can use this to check of (x-a) is a factor of polynomial. If f(a) = 0, that means the remainder is 0, indicating that (x-a) is a factor of the polynomial.