Calculus-Remainder Theorem

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

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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 thats 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
$$(m-4)*(m^2-m+2)=0$$

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