If the polynomial x5 − 105 can be split as the product of the polynomials x − 10 and a, what is a? x4 − 99,990 x4 + 10x3 + 100x2 + 1,000x − 10,000 x4 + 10x3 + 100x2 + 1,000x + 10,000

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FadaKen FadaKen · Answer 1 · 2017-05-02T22:58:09+02:00

x^4+10x^3+100x^2+1000x+10000

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parmesanchilliwack parmesanchilliwack · Answer 2 · 2019-04-09T09:50:51+02:00

Answer:

[tex]x^4 + 10x^3 + 100x^2 + 1,000x + 10,000[/tex]

Step-by-step explanation:

Here, the given polynomial,

[tex]x^5-10^5[/tex]

Since, it can be split as the product of the polynomials x − 10 and a,

So, we can write,

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

[tex]\implies a = \frac{x^5-10^5}{x-10}[/tex]

By the long division ( shown below ),

We get,

[tex]a=x^4 + 10x^3 + 100x^2 + 1,000x + 10,000[/tex]

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