1. ## Remainder theorum

Determine the remainder when x³-6x²+x-5 is divided by:
a. X+2
b. X-3

Hi I was wondering if someone can help me with these revision questions.

2. ## Re: Remainder theorum

Originally Posted by Andrew187
Determine the remainder when x³-6x²+x-5 is divided by:
a. X+2
b. X-3.

If $\displaystyle f(x)=x^3-6x^2+x-5$ then if $\displaystyle f(a)=0$ then $\displaystyle (x-a)$ is a factor, so it divides $\displaystyle f(x)$.

Thus what is $\displaystyle f(-2)~\&~f(3)~?$

3. ## Re: Remainder theorum

f(x) = x³ - 6x² + x - 5

(x+2)= f(-2) = (-2)³ - 6(-2)² + (-2) - 5 =

-8 - 24 - 2 - 5 = -39

Is this correct? I can't work out the answer for the first formula

4. ## Re: Remainder theorum

Originally Posted by Plato
If $\displaystyle f(x)=x^2-6x^2+x-5$ then if $\displaystyle f(a)=0$ then $\displaystyle (x-a)$ is a factor, so it divides $\displaystyle f(x)$.

Thus what is $\displaystyle f(-2)~\&~f(3)~?$
That actually doesn't help the OP.

The remainder theorem states that for a polynomial function P(x) is divided by (x - a), the remainder is equal to P(a).

5. ## Re: Remainder theorum

Originally Posted by Andrew187
f(x) = x³ - 6x² + x - 5
(x+2)= f(-2) = (-2)³ - 6(-2)² + (-2) - 5 =
-8 - 24 - 2 - 5 = -39
Is this correct? I can't work out the answer for the first formula
Yes that is correct.
Thus $\displaystyle (x+2)$ does not divide $\displaystyle f(x)$. So $\displaystyle -39$ must be the remainder.

Surely you can find $\displaystyle (3)^3-6(3)^2+(3)-5=~?$

6. ## Re: Remainder theorum

Originally Posted by Plato
Yes that is correct.
Thus $\displaystyle (x+2)$ does not divide $\displaystyle f(x)$. So $\displaystyle -39$ must be the remainder.

Surely you can find $\displaystyle (3)^3-6(3)^2+(3)-5=~?$
its -29

But how come your formula is different to my first formula have I wrote it wrong?

7. ## Re: Remainder theorum

Originally Posted by Andrew187
But how come your formula is different to my first formula ?
How is it different?

8. ## Re: Remainder theorum

Originally Posted by Plato
Yes that is correct.
Thus $\displaystyle (x+2)$ does not divide $\displaystyle f(x)$. So $\displaystyle -39$ must be the remainder.

Surely you can find $\displaystyle (3)^3-6(3)^2+(3)-5=~?$
Is that sum for (x-3)?

9. ## Re: Remainder theorum

Originally Posted by Andrew187
Is that sum for (x-3)?

That is the remainder when $\displaystyle f(x)=x^3-6x^2+x-5$ is divided by $\displaystyle (x-3)$.

10. ## Re: Remainder theorum

Originally Posted by Plato
Yes that is correct.
Thus $\displaystyle (x+2)$ does not divide $\displaystyle f(x)$. So $\displaystyle -39$ must be the remainder.

Surely you can find $\displaystyle (3)^3-6(3)^2+(3)-5=~?$
27-24+3-5=1 is this correct?
or is it this 27-72+3-5= -43