Find the remainder of the division of
2 answers:
<h3>Answer: C) 77</h3>
Remainder theorem: If p(x) is divided by (x-k), then the remainder is p(k)
In our case, p(x) = x^3-5x^2-4x+7 and k = 7
p(x) = x^3-5x^2-4x+7
p(7) = (7)^3-5(7)^2-4(7)+7
p(7) = 77
The remainder is 77
Side note: The nonzero remainder means x-7 is not a factor of x^3-5x^2-4x+7.
You can also use polynomial long division (see figure 1) or synthetic division (see figure 2). The figures are attached in the image below.
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If the function is and f(4) − f(1) = f '(c)(4 − 1) then there is not any answer.
Given function is and f(4) − f(1) = f '(c)(4 − 1).
In this question we have to apply the mean value theorem, which says that given a secant line between points A and B, there is at least a point C that belongs to the curve and the derivative of that curve exists.
We begin by calculating f(2) and f(5):
f(2)=
f(2)=1
f(5)=
f(5)=1
And the slope of the function:
(x)=
(c)=0
Now,
=-2
=0
-2 is not equal to 0. So there is not any answer.
Hence if the function is and f(4) − f(1) = f '(c)(4 − 1) then there is not any answer.
Learn more about derivatives at brainly.com/question/23819325
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