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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If 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
 one year ago
Best ResponseYou've already chosen the best response.0So, either dw:1436819332290:dw or you can evaluate \((4)^33(4)^213(4)+78.\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Not quite. I think you made an arithmetic mistake.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[(4)^33(4)^213(4)+78=6448+52+78=4+14=18\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Also, if you were to do the synthetic method (which I think is easier for these bigger numbers, you'd get:dw:1436819716328:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes thank you so much

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you help me with one more

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Which of the following is a factor of f(x) = 4x3 + 11x2 − 75x + 18? my answer was (x+3)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What were your other choices?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(x − 3) (x + 3) (x − 1 over 3) (x + 1 over 3)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Before 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
 one year ago
Best ResponseYou've already chosen the best response.0Synthetic 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
 one year ago
Best ResponseYou've already chosen the best response.0Next, 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
 one year ago
Best ResponseYou've already chosen the best response.0Add 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
 one year ago
Best ResponseYou've already chosen the best response.0So, since 234 ≠ 0, x + 3 isn't a factor. So, now, try using x3, and do what I did above and see how you do. I'll set it up for you.\[x3=0\]\[x=3\]dw:1436820965654:dw Can you take it from there?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, because the remainder becomes 0.dw:1436821132952:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.018  18 is 0, so yes, x  3 is a factor.
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