Use the remainder theorem to find which of the following is not a factor of x3 + 12x2 + 47x + 60
the answer is x-5 but idk why
The remainder theorem states that
f(x) = (x-p)*q(x) + f(p)
So, if f(p)=0, (x-p) divides f(x) evenly; it is a factor.
f(5) = 5^3 + 12*5^2 + 47*5 + 60 = 720
so, f(x) = (x-5)*q(x) + 720
for some q(x)
To determine if x - 5 is a factor of the polynomial x^3 + 12x^2 + 47x + 60, we can use the remainder theorem. The remainder theorem states that if a polynomial f(x) is divided by x - a, then the remainder is equal to f(a).
To apply the remainder theorem, substitute x = 5 into the polynomial:
f(5) = (5)^3 + 12(5)^2 + 47(5) + 60
= 125 + 300 + 235 + 60
= 720
If the result is zero, then x - 5 is a factor. However, since f(5) = 720, which is not equal to zero, x - 5 is not a factor of the given polynomial x^3 + 12x^2 + 47x + 60.
Therefore, the answer to the question is x - 5 is not a factor of x^3 + 12x^2 + 47x + 60.