1. f(x) = 1
2. f(x) = x
3. f(x) = 5 - x
4. f(x) = 3
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.
All you have to is divide two consecutive terms to calculate the common ratio
1/4 divided by 5/12 = 1/4 * 12/5 = 12/20 = 3/5
