## anonymous one year ago What is the remainder when (x3 − 3x2 − 13x + 78) is divided by (x + 4)?

1. anonymous

If you know synthetic division, you can just use that to figure out the remainder. However, if you don't you can plug in x = -4 to find the remainder.

2. anonymous

So, either |dw:1436819332290:dw| or you can evaluate \((-4)^3-3(-4)^2-13(-4)+78.\)

3. anonymous

ok give me a sec

4. anonymous

o ok . o its 15

5. anonymous

so*

6. anonymous

Not quite. I think you made an arithmetic mistake.

7. anonymous

\[(-4)^3-3(-4)^2-13(-4)+78=-64-48+52+78=4+14=18\]

8. anonymous

oooooo

9. anonymous

Also, if you were to do the synthetic method (which I think is easier for these bigger numbers, you'd get:|dw:1436819716328:dw|

10. anonymous

Do you get it?

11. anonymous

yes thank you so much

12. anonymous

No problem.

13. anonymous

can you help me with one more

14. anonymous

Sure.

15. anonymous

Which of the following is a factor of f(x) = 4x3 + 11x2 − 75x + 18? my answer was (x+3)

16. anonymous

17. anonymous

(x − 3) (x + 3) (x − 1 over 3) (x + 1 over 3)

18. anonymous

Before I explain this, do you know how to do synthetic division? If not, it'd probably be better for me to explain how to do that first.

19. anonymous

ok explain plz

20. anonymous

Synthetic division basically lets you divide polynomials. So, you can see whether something is a factor of something else. Let's do it with this question. You said your answer was x + 3. Start off by setting the "factor" or what you're dividing equal to 0. So:\[x+3=0\]Now, solve for x.\[x=-3\]This is the number you're going to be using. Now, set up the question like this.|dw:1436820455972:dw| If you look, the numbers on the top are the coefficients next to the 'x'.

21. anonymous

Next, bring down the first number at the top.|dw:1436820595855:dw| Then, multiply this number by the number in the top left corner and place that number in the next column like so.|dw:1436820628993:dw|

22. anonymous

Add the two numbers in the column, and then bring down the sum and repeat.|dw:1436820714464:dw| If the remainder isn't 0, it isn't a factor.

23. anonymous

ooooooooo

24. anonymous

So, since 234 ≠ 0, x + 3 isn't a factor. So, now, try using x-3, and do what I did above and see how you do. I'll set it up for you.\[x-3=0\]\[x=3\]|dw:1436820965654:dw| Can you take it from there?

25. anonymous

so its A

26. anonymous

Yes, because the remainder becomes 0.|dw:1436821132952:dw|

27. anonymous

18 - 18 is 0, so yes, x - 3 is a factor.