1. ## Remanider Theorem

Hello everyone, I am studying Engineering Mathematics and have a maths test Tuesday.. I have been given some example questions several of which include the remainder theorem..

Please could someone show me the way with the following example.

(I do have notes that refer to ap sqaured + bp + c but unfortunately my class notes are poor)

3xsquared + 11x -8 divided by x+5

I'm off to try it somemore myself but ill keep checking back here, thanks all

(3)(-5)squared + (11)(-5) - 8 =12

3. Originally Posted by HNCMATHS
Hello everyone, I am studying Engineering Mathematics and have a maths test Tuesday.. I have been given some example questions several of which include the remainder theorem..

Please could someone show me the way with the following example.

(I do have notes that refer to ap sqaured + bp + c but unfortunately my class notes are poor)

3xsquared + 11x -8 divided by x+5

I'm off to try it somemore myself but ill keep checking back here, thanks all
Hi HNCMATHS,

$\displaystyle (3x^2+11x-8) \div (x+5)$

If you want to just divide, you might consider synthetic division. Are you familiar with this?

If not, can you do polynomial long division?

If you're just trying to find the remainder, do this:

$\displaystyle f(-5)=3(-5)^2+11(-5)-8$

$\displaystyle f(-5)=12$

4. Hello there!

Thanks very much for the reply, unfortunately i have to use the remainder theorem to prove i understand the 'remainder theorem'

i think i have worked it out kinda, could you take a look at my own reply to this ?

5. Originally Posted by HNCMATHS
Hello there!

Thanks very much for the reply, unfortunately i have to use the remainder theorem to prove i understand the 'remainder theorem'

i think i have worked it out kinda, could you take a look at my own reply to this ?
Your solution is the same as mine.

6. $\displaystyle \frac{p(x)}{x-a}=q(x)+Rem$

$\displaystyle p(x)=(x-a)q(x)+Rem$

Therefore

$\displaystyle p(a)=Rem$

Hence

$\displaystyle [p(x)-Rem]$ is evenly divisible by $\displaystyle x-a$

7. ## Another One

Yes thank you Masters,

If you dont mind could you help me with this next one its the divisor which is different and is making it hard for me...

$\displaystyle x^3 - x^2 +2x + 4 \div (2x + 1)$

8. The denominator is $\displaystyle 2(x-[-0.5])$

Placing x=-0.5 into the numerator $\displaystyle x^3-x^2+2x+4$ gives the remainder

9. Hello Archie,

Unfortunately i dont follow

I need to use the methods previous shown, i.e remainder theorem

regards,

chris

10. Archie following your reply with 0.5 i have worked it out!!!!!

excellent!

Thanks so much

11. Originally Posted by HNCMATHS
Yes thank you Masters,

If you dont mind could you help me with this next one its the divisor which is different and is making it hard for me...

$\displaystyle x^3 - x^2 +2x + 4 \div (2x + 1)$
Simply put, if you want to find the remainder, set the divisor = 0 and solve for x.

$\displaystyle 2x+1=0$

$\displaystyle x=-\frac{1}{2}$

Then, $\displaystyle f\left(-\frac{1}{2}\right)$ will give you the remainder.

12. Thank you both so much, what a fantastic site!

13. Well done Chris!