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

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

ilovepuppieslol · Answer

the multiplication of $a$ with $(x-10)$ must give $(x^5-105)$ as product

so

$a \times (x-10)=x^5-105$

$a=\large \frac{x^5-105}{x-10}$

do this division to get your solution! :)