QUESTIONS - POLYNOMIALS

QUESTIONS - ANSWERS - POLYNOMIALS
On 11/12/06, Hope wrote:
> Hope has left a new comment on your post "Questions - Differential
> Equations":
>
> How do you do this? Divide x+3 into 2x^3+7x^2+x+3. Give the remainder and
> tell whether x+3 is a factor.
Remainder theorem helps to find remainder and hence whether a
particular binomial is a factor or not.But we cant get quotient from
it.
PUT X+3 =0..X=-3
DIVIDE USING SHORT DIVISION
-3|2 +7 +1 +3
0 -6 -3 +6
----------------------------
2 +1 -2 +9.............REMAINDER =9
QUOTIENT IS.... 2X^2 +X -2
X+3 IS NOT A FACTOR AS REMAINDER IS NOT ZERO.USING REMAINDER THEOREM
REMAINDER = F(-3) =
2*(-3)^3 +7(-3)^2+(-3)+3
=-54+63-3+3=9=REMAINDER


In the problem above, for what
> value of x does 2x^3+7x^2+x+3 equal 9? Find the solution w/o using direct
> substitution if you can, and explain your answer in terms of the remainder
> theorem.
AS WE SAW WITH REMAINDER THEOREM F(-3) = 9
SO FOR X=-3, WE GET F(-3) =9.
IF YOU DONT WANT DIRECT SUBSTITUTION, THEN THE DIVISION DONE ABOVE
GIVES F(-3) =9
BUT YOUR QUESTION SEEMS TO BE LITTLE ODD AND THE OBJECTIVE IS NOT CLEAR.