leahstubbs
19.11.2020 •
Mathematics
Free points. uwu. What's your favorite color?
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Ответ:
red :)
Step-by-step explanation:
give brainliest pls so i can reach my goal
Ответ:
my favorite color is blue and red
Step-by-step explanation:
Ответ:
1. The remainder is 2·x² - x + 4
2. The polynomial is 12·x⁵ + 30·x⁴ + 20·x³
Step-by-step explanation:
Here we have that the polynomial is to be divided by x(x-1)(x-2) with a remainder, hence the polynomial should be at least degree 3
Therefore
Therefore, f(x) = g(x)·x·(x-1)·(x-2)+a·x² + b·x + c
We substitute the values of x and f(x) to get
f(0) = c = 4
f(1) = a + b + 4 = 5 which gives a + b = 1.......................(1)
f(2) = 4·a + 2·b + 4 = 10 which gives 4·a + 2·b = 6----(2)
Multiplying equation (1) by 2 and subtracting it from equation (2), we get
2·a = 4
a = 2 ∴ b = 1 - 2 = -1
Hence, f(x) divided by x·(x-1)·(x-2), the remainder = 2·x² - x + 4
2. Here we have
f(x) is divisible by x³ gives
f(x) = x³(ex² + fx + g) = e·x⁵ + f·x⁴ + g·x³
and f(x) + 2 = (x + 1)³(a·x² + b·x +c) = a·x⁵ + (3·a+b)·x⁴ + (3·a+3·b+c)·x³ + (a+3·b+3·c)·x² + (b+3·c)·x + c
f(x) = (x + 1)³(a·x² + b·x +c) = a·x⁵ + (3·a+b)·x⁴ + (3·a+3·b+c)·x³ + (a+3·b+3·c)·x² + (b+3·c)·x + c - 2
Therefore, the coefficients of x², x and the constants are equal to 0
We have
a+3·b+3·c = 0
b+3·c = 0
c - 2 = 0
Hence, c = 2, b = -6, a = 12
Therefore the polynomial = 12·a⁵ + 30·x⁴ + 20·x³.