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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.
So, either |dw:1436819332290:dw| or you can evaluate \((-4)^3-3(-4)^2-13(-4)+78.\)
ok give me a sec
o ok . o its 15
Not quite. I think you made an arithmetic mistake.
Also, if you were to do the synthetic method (which I think is easier for these bigger numbers, you'd get:|dw:1436819716328:dw|
Do you get it?
yes thank you so much
can you help me with one more
Which of the following is a factor of f(x) = 4x3 + 11x2 − 75x + 18? my answer was (x+3)
What were your other choices?
(x − 3) (x + 3) (x − 1 over 3) (x + 1 over 3)
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.
ok explain plz
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'.
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|
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.
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?
so its A
Yes, because the remainder becomes 0.|dw:1436821132952:dw|
18 - 18 is 0, so yes, x - 3 is a factor.