polynomial quadradic function? :s

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Szafranko

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Apr 18, 2010
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hello first post, with a little bit of math problem here
my name is patrick, i am in grade 12 and my teacher sucks at teaching lol, so i dont get how to do this properly.. if someone could help point out step by step what to do? that'd be nice

So we have

2x^2 + kx -5 divided by x-3 remainder is 7
determine the value of k

i have no idea where to start.

p.s sorry about posting in geometry that just made no sense now that i think about it.
 
Okay, I replied to your other thread, but in-case that thread gets deleted because it is in the wrong section I'll post my reply here as well.

If you know how to perform synthetic division, than you can figure out what k is.

3 | 2 k -5
_ | _ ? _ ?
_ _ 2 ? _ 7

Fill in the question marks.
 
ok i get synthetic division. but i'm having trouble.. so lets see

i like better visuals perhaps thats the confusion here..

3 | 2 k -5
|____6___?____
2 ?! 7

thats how far im getting with what i can only try to understand..
so .. how does this help? :s no offense to you trying to help me but i dont see how i can solve for k... unless.... ?

3 | 2 k -5
|____6___12____ i do it in reverse from the remainder? making k+6 = 4... when 12 is divided by 3...
2 ?! 7

making k -2!?!

lets see if it fits..

3| 2 -2 -5
|_____6___12___
2 4 7


ahhh SUCCESS!!! THANK YOU!
 
Szafranko said:
hello first post, with a little bit of math problem here
my name is patrick, i am in grade 12 and my teacher sucks at teaching lol, so i dont get how to do this properly.. if someone could help point out step by step what to do? that'd be nice

So we have

2x^2 + kx -5 divided by x-3 remainder is 7
determine the value of k

i have no idea where to start.

p.s sorry about posting in geometry that just made no sense now that i think about it.
Click to expand...

This problem is rather easily done using the Remainder Theorem:

When a polynomial function f(x) is divided by (x - a), the REMAINDER for the division is f(a)

For example, if I want to know what the remainder is when f(x) = x[sup:23oh4izy]3[/sup:23oh4izy] - 3x[sup:23oh4izy]2[/sup:23oh4izy] + 5x - 1 is divided by (x - 2), all I need to do is find f(2):

f(2) = 2[sup:23oh4izy]3[/sup:23oh4izy] - 3(2)[sup:23oh4izy]2[/sup:23oh4izy] + 5(2) - 1
f(2) = 8 -12 + 10 - 1
f(2) = 5

(you may want to try that with either synthetic division or long division to see if you agree!)

So, you've got

f(x) = 2x[sup:23oh4izy]2[/sup:23oh4izy] + kx - 5

You know that the remainder when f(x) is divided by (x - 3) is 7. The Remainder Theorem tells us that the remainder when f(x) is divided by (x - 3) is f(3).....

f(3) = 7
f(3) = 2(3][sup:23oh4izy]2[/sup:23oh4izy] + k(3) - 5
f(3) = 18 + 3k - 5
But we already KNOW from the Remainder Theorem that f(3) = 7. So,

18 + 3k - 5 = 7
13 + 3k = 7
3k = -6
k = -2

Check by dividing 2x[sup:23oh4izy]2[/sup:23oh4izy] - 2x - 5 by (x - 3)....see if you get a remainder of 7.
 
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