Answer:
Explanation:
The answer choices are:
The remainder theorem states that the remainder of the division of a polynomial f(x) by a factor x - a is equal to f(a).
Therefore, when f(a) = 0, the remainder is zero and x - a is a factor of the polynomial.
Then, you must find f(a) for each of the factors on the choices:
a. x + 5
⇒ a = - 5
[tex]f(-5)=(-5)^3+12(-5)^2+47(-5)+60=-125+300-235+60=0[/tex]
Since f(-5) = 0, x + 5 is a factor of the polynomial.
b. x + 4
⇒ a = - 4
[tex]f(-4)=(-4)^3+12(-4)^2+47(-4)+60=-64+192-188+60=0[/tex]
Since f(-4) = 0, x + 4 is a factor.
c. x + 3
[tex]f(-3)=(-3)^3+12(-3)^2+47(-3)+60=-27+108-141+60=0[/tex]
Since f(-3) = 0, x + 3 is a factor.
d. x + 2
[tex]f(-2)=(-4)^3+12(-2)^2+47(-2)+60=-8+48-94+60=6[/tex]
Since f(-2) ≠ 0, x + 2 is not a factor ← answer
