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

Question

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

Miss Alice Doyle · Accepted Answer

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

Miss Alice Doyle · Answer

Step-by-step explanation:Here, the given polynomial, Since, it can be split as the product of the polynomials x − 10 and a,So, we can write,By the long division ( shown below ), We get,

Miss Alice Doyle · Answer

Value of a is:Step-by-step explanation:we know that:Here, a=10 and n=5⇒ Hence,Value of a is:

Miss Alice Doyle · Answer

Hello,using synthetic division,

Miss Alice Doyle · Answer

To answer this item, all that needs to be done is dividing the mathematical expression of x⁵ - 10⁵, our dividend, by x - 10, which is our divisor. The mathematical expression that can be used in order to properly express the given scenario is,                        x⁵ - 10⁵ = (x - 10)(a)The value of a, as stated above, can be calculated by the equation,                     a = (x⁵ -10⁵) / (x - 10)There are two ways to solve the problem: synthetic division and the long way. Each of which will yield the same answer. Simplifying the value of a will give us a final answer of,      a = x⁴ + 10x³ + 100x² + 1000x

Natalie Goodwin

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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