+0

# Polynomial remaindery stuff.

0
305
3

idk if the upload of the picture worked (if it didnt someone help me understand how to use it)

Find k if the remainder is 3 when 5x^2-10x+k is divided by x-1

I have several questions like this one so im more looking for an explanation than a solution :) thank you!

Guest Jun 1, 2015

#2
+26403
+10

If 5x2 - 10x + k has remainder 3 when divided by x - 1 then we must have:

5x2 - 10x + k = (x - 1)*m + 3  where m is an integer.

When x = 1 the right-hand side is just 3 and m disappears so put x = 1 in the left-hand side as well to get

5 - 10 + k = 3

or k = 8

(Chris beat me to it!)

Incidentally, you can't upload images as long as you stay Anonymous.  Why not register, then you will have access to the upload images function.

.

Alan  Jun 1, 2015
Sort:

#1
+81029
+10

Notice that if we substituted 1 into the polynomial, we could find the value of k that would make 1 a root....in other words, we could find the k value such that, P(1) = 0....... (or, put another way, would make (x-1) a divisor of the polynomial with no remainder).......

So.....using the same idea.......we want to find the value of k that makes P(1)  = 3

So P(1)  =  5(1)^2 - 10(1) + k = 3   →  5 - 10 + k = 3  →  -5 + k = 3 →  k = 8

Test this for yourself using synthetic division.......you will find that you get a remainder of 3 when k = 8 and you divide by 1.....

CPhill  Jun 1, 2015
#2
+26403
+10

If 5x2 - 10x + k has remainder 3 when divided by x - 1 then we must have:

5x2 - 10x + k = (x - 1)*m + 3  where m is an integer.

When x = 1 the right-hand side is just 3 and m disappears so put x = 1 in the left-hand side as well to get

5 - 10 + k = 3

or k = 8

(Chris beat me to it!)

Incidentally, you can't upload images as long as you stay Anonymous.  Why not register, then you will have access to the upload images function.

.

Alan  Jun 1, 2015
#3
+81029
0

That's OK, Alan.....you gave me 3 points....I'll give you 3......!!!

CPhill  Jun 1, 2015

### 4 Online Users

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