## blahblah_who_cares 2 years ago Find the remainder if P(x)=x^3+17 is divided by (x+2).

1. DarthTony

9 ?

2. blahblah_who_cares

The answer is 9, but I dont understand how to get it.

3. blahblah_who_cares

@DarthTony

4. Directrix

@blahblah_who_cares Have you studied synthetic division or the Remainder Theorem?

5. blahblah_who_cares

I have.

6. Directrix

Remainder Theorem?

7. blahblah_who_cares

No. Just synthetic. And I might have learned Remainder but I dont recall anything like it. .

8. dumbcow

for (x+2) evaluate f(-2) to get remainder

9. Directrix

We can do either here. I will post the Remainder Theorem so that you can tell me if you've ever seen it. Regardless, we will do the problem but will use the method you have studied. Tell me which method after you look at this remainder theorem. Remainder Theorem If a polynomial P( x) is divided by ( x – r), then the remainder of this division is the same as evaluating P( r), and evaluating P( r) for some polynomial P( x) is the same as finding the remainder of P( x) divided by ( x – r).

10. Directrix

@blahblah_who_cares

11. blahblah_who_cares

Yah. Ive never learned Remainder Theorem. @Directrix

12. Directrix

We'll do synthetic division.

13. Directrix

P(x)=x^3+17 is divided by (x+2) P(x) = x^3 + 0x^2 + 0x + 17 divided by (x + 2) |dw:1360114222669:dw|

14. Directrix

Does that look familiar?

15. blahblah_who_cares

Ok. So i think my big question here is how to get the -2.

16. Directrix

|dw:1360114478786:dw|

17. Directrix

Consider this example: Example 1 Find P(–3) if P( x) = 7 x5 – 4 x3 + 2 x –11. There are two methods of finding P(–3). • Method 1: Directly replace –3 for x. • Method 2: Find the remainder of P( x) divided by [ x – (–3)].

18. blahblah_who_cares

No. I mean how did you get -2 from (x+2).

19. Directrix

If the divisor is (x +2), for synthetic division, it is written as (x - (-2)) which results in a divisor of (-2).

20. blahblah_who_cares

Oh.. Ok. thanks.