Question

Which of the following is the binomial factor in the factorization of m ^15 - 1,000?

m5 - 10
m5 + 10
m5 + 100
m3 + 10

Answer 1

`Use\ (a^n)^m=a^(nm)\ and\ a^3-b^3=(a-b)(a^2+ab+b^2).\\\\m^(15)=m^(5\cdot3)=(m^5)^3\\\\m^(15)-1,000=(m^5)^3-10^3=(m^5-10)[(m^5)^2+(m^5)(10)+10^2]\\\\=(m^5-10)(m^(10)+10m^5+100)\\\\Answer:\ \boxed{m^5-10}`