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helpmewithmath70
12.07.2019 •
Mathematics
Find the least common multiple of x 3 - x 2 + x - 1 and x 2 - 1. write the answer in factored form. a. (x + 1) 2(x - 1) b. (x + 1)(x - 1)(x 2 + 1) c. (x 3 - x 2 + x - 1)(x 2 - 1) d. (x + 1)(x - 1)(x 2 - 1)
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Ответ:
f(x) = x³ - x² + x - 1
g(x) = x² - 1
By the remainder theorem, f(1) = 1 -1 + 1 - 1 = 0
Therefore (x-1) is a factor.
Perform synthetic division.
1 | 1 -1 1 -1
1 0 1
1 0 1 0
Therefore,
f(x) = (x-1)(x²+1)
Also,
g(x) = (x+1)(x-1)
b.
The least common multiple for f(x) and g(x) is (x + 1)(x - 1)(x² + 1).
Ответ:
Time. Water
0.5. 0.8
1. 1.6
3. 4.8
25. 40