Yes. When the function f(x) = x3 – 75x + 250 is divided by x + 10, the remainder is zero. Therefore, x + 10 is a factor of f(x) = x3 – 75x + 250.
According to the remainder theorem when f(x) is divided by (x+a) the remainder is f(-a). In this case, f(x)=x^3-75x+250 (x+a)=(x+10) Therefore, the remainder f(-a)=f(-10)
=x^3-75x+250 =(-10)^3-(75*-10)+250 =-1000+750+250 =1000-1000 =0. The remainder is 0. So, (x+10) is a factor of x^3-75x+250.
