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**+10 **

If 5x^{2} - 10x + k has remainder 3 when divided by x - 1 then we must have:

5x^{2} - 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

#1**+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**+10 **

Best Answer

If 5x^{2} - 10x + k has remainder 3 when divided by x - 1 then we must have:

5x^{2} - 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