christifer71 christifer71
  • 01-09-2017
  • Mathematics
contestada

If the polynomial x5 − 105 can be split as the product of the polynomials x − 10 and a, what is a?

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caylus
caylus caylus
  • 01-09-2017
Hello,

using synthetic division,
[tex]x^5-10^5=(x-10)(x^4+10x^3+100x^2+1000x+10000). [/tex]
Answer Link
erato erato
  • 19-07-2019

Answer:

Value of a is:

[tex]x^4+10x^3+100x^2+1000x+10000[/tex]

Step-by-step explanation:

we know that:

[tex]x^n-a^n=(x-a)(x^{n-1}+ax^{n-2}+a^2x^{n-3}+...+a^{n-2}x+a^{n-1})[/tex]

Here, a=10 and n=5

[tex]x^5-10^5=(x-10)(x^4+10x^3+100x^2+1000x+10000)[/tex]

[tex]x^5-10^5=(x-10)a[/tex]

⇒ [tex]a=x^4+10x^3+100x^2+1000x+10000[/tex]

Hence,Value of a is:

[tex]x^4+10x^3+100x^2+1000x+10000[/tex]

Answer Link

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