Answer:
Answers: A and D. (first and last choice.)
Step-by-step explanation:
f(x) = x^3(x + 5) - x(x + 5) On each side of the minus sign, there is a common factor of (x + 5). Using the distributive property we can take out the common fact to get
f(x) = (x + 5) ( x^3 - x)
the second factor (x^3 - x) can also take out a common factor of x. That gives this factor of x(x^2 - 1) and from that we get x (x + 1)(x - 1) So f(x)=x*(x+1)(x - 1)(x+5)
Now let's see what they are asking for.
If you divide by x + 5 that divides evenly and so there is no remainder. The top one is correct.
The second one is false. It will not divide evenly into the given equation. x - 5 is not a factor.
The second one would have to be true if the third one is to be true. Since the second one is false, so is this one.
Since the first one is true, so is this one.
