polynomial?

[Szafranko]

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
I am not sure which forum this apply's to but i think it's polynomial functions. involving some remainder theory and dividing with sum functions thrown in just for hoots...

So we have

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

 

[bashbobhash]

Well, if you know how to do synthetic division, you can figure out what k is, since you know what the remainder is supposed to be.


2x^2 + kx -5 over x-3 gives you a remainder of 7.

3 | 2______ k______-5
__| _______??______??
____2______??______7

Fill in the blanks, and you'll figure out what k is.

 

[BigGlenntheHeavy]

\(\displaystyle f(x) \ = \ 2x^2+kx-5, \ Remainder \ theorem \ \implies \ that \ f(3) \ = \ 7,\)

\(\displaystyle hence \ f(3) \ = \ 7 \ = \ 18 +3k-5, \ 7 \ = \ 13+3k, \ 3k \ = \ -6, \ k \ = \ -2\)

\(\displaystyle And, \ yes, \ lad, \ it \ is \ a \ polynomial.\)