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lizzy2951
21.07.2020 •
Mathematics
Problem P(x)=x4−3x2+kx−2P(x)=x^4-3x^2+kx-2P(x)=x4−3x2+kx−2P, left parenthesis, x, right parenthesis, equals, x, start superscript, 4, end superscript, minus, 3, x, squared, plus, k, x, minus, 2 where is an unknown integer. P(x)P(x)P(x)P, left parenthesis, x, right parenthesis divided by (x−2)(x-2)(x−2)left parenthesis, x, minus, 2, right parenthesis has a remainder of 10101010. What is the value of ? K=k=k=
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Ответ:
k = 4
Step-by-step explanation:
For this division, to determine the value of k, use the Remainder Theorem, which states that:
polynomial p(x) = dividend (x-a) * quotient Q(x) + remainder R(x)
Knowing the degree of quotient is
degree of Q = degree of p(x) - degree of (x-a)
For this case, Q(x) is a third degree polynomial.
Using the theorem:
a = 1
b - 2a = 0 ⇒ b = 2
c - 2b = -3 ⇒ c = 1
-2d + 10 = -2 ⇒ d = 6
d - 2c = k ⇒ k = 4
Therefore, k = 4 and Q(x) =![x^{4} -2x^{2} + 4x + 2](/tpl/images/0710/5631/3b809.png)
Ответ:
200 or 1 length
Step-by-step explanation: