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vlada-n [284]
2 years ago
14

Is x-2 a factor of 4x^5 +5x^4 +1?

Mathematics
1 answer:
nordsb [41]2 years ago
8 0

Answer:

No

Step-by-step explanation:

By the Factor theorem

If (x - h) is a factor of f(x) then f(h) = 0

Here (x - 2) with h = 2 and f(x) = 4x^{5} + 5x^{4} + 1 , then

f(2) = 4(2)^{5} + 5(2)^{4} + 1

     = 4(32) + 5(16) + 1

     = 128 + 80 + 1

     = 209

Since f(2) ≠ 0 then ( x - 2) is not a factor

 

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Answer:

The mean is also increased by the constant k.

Step-by-step explanation:

Suppose that we have the set of N elements

{x₁, x₂, x₃, ..., xₙ}

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M = (x₁ + x₂ + x₃ + ... + xₙ)/N

Now if we increase each element of our set by a constant K, then our new set is:

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The mean of this set is:

M' = ( (x₁ + k) + (x₂ + k) + ... + (xₙ + k))/N

M' = (x₁ + x₂ + ... + xₙ + N*k)/N

We can rewrite this as:

M' = (x₁ + x₂ + ... + xₙ)/N + (k*N)/N

and  (x₁ + x₂ + ... + xₙ)/N was the original mean, then:

M' = M + (k*N)/N

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Step-by-step explanation:

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