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lbvjy [14]
3 years ago
15

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

Mathematics
2 answers:
katrin2010 [14]3 years ago
3 0
X^4+10x^3+100x^2+1000x+10000
nordsb [41]3 years ago
3 0

Answer:

x^4 + 10x^3 + 100x^2 + 1,000x + 10,000

Step-by-step explanation:

Here, the given polynomial,

x^5-10^5

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

So, we can write,

a(x-10) = x^5-10^5

\implies a = \frac{x^5-10^5}{x-10}

By the long division ( shown below ),

We get,

a=x^4 + 10x^3 + 100x^2 + 1,000x + 10,000

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