How Do You Solve for m in a Polynomial Division Problem?

[thomasrules]

Find the value of m so that when x^3+5x^2+6x+11 is divided by (x+m) the remainder is 3.

Im having so much diffculty with this and it's so frustrating can anyoen help

Thomas

 

[wisredz]

Do you know how to divide polynomials? For example if you divide ax^2+bx+c by (x+d) what would be the remainder? There's an easy way for doing this. find value of d which makes x+d=0. Then replace that value with x in the original polynomial equation, and what you got is the remainder of division!

Try doing this and let me know if there's any problem

 

[thomasrules]

Sorry but I'm still not clear on that. I know that to find a value that's divisible in an equation you try f(x) and if that equals 0 in the equation its divisible. In my case its x^3+5x^2+6x+11 so the only things i try are the last number 11. (+-1, +-11) and that doesn't equal 0...Explain more please

 

[wisredz]

You divide the equation by (x+m) right? What I'm telling that find the root of this function (x+m, that is) and then place the root into the polynomial. Then you will have the remainder, which is 3. Solve for m and you got it!

The root for x+m=0 is obviously -m. now place -m in the place of x in the equation x^3+5x^2+6x+11. What I tell you is that setting x=-m in this equation gives you the remainder when you divide x^3+5x^2+6x+11 by (x+m).

 

[thomasrules]

omg dude no I get another answer...can you tell me your answer if it's so easy lol

 

[wisredz]

Is it 4? If not there should be something wrong with the answer...

 

[himanshu121]

yup,
f(x)=g(x)(x+m) +R
put x=-m
u will get
after rearranging
$$m^3 - 5m^2+6m-8=0$$
solving u will have
$$(m-4)*(m^2-m+2)=0$$