What is the remainder when (x3 − 3x2 − 13x + 78) is divided by (x + 4)?

- anonymous

What is the remainder when (x3 − 3x2 − 13x + 78) is divided by (x + 4)?

- chestercat

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- 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.

- anonymous

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

- anonymous

ok give me a sec

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- anonymous

o ok . o its 15

- anonymous

so*

- anonymous

Not quite. I think you made an arithmetic mistake.

- anonymous

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

- anonymous

oooooo

- 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|

- anonymous

Do you get it?

- anonymous

yes thank you so much

- anonymous

No problem.

- anonymous

can you help me with one more

- anonymous

Sure.

- anonymous

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

- anonymous

What were your other choices?

- anonymous

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

- 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.

- anonymous

ok explain plz

- 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'.

- 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|

- 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.

- anonymous

ooooooooo

- 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?

- anonymous

so its A

- anonymous

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

- anonymous

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

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