Which statements are true about the polynomial function?
f(x)=x3+5x2+6x
Select each correct answer.
f(x)=0 when x=2 .
(x+2) is a factor of f(x) .
f(x) divided by (x−2) has a remainder of 0.
f(−2)=0
+128408 f(x)=x^3+5x^2+6x
Let's examine each statement
First one
When x = 2 f(2) = (2)^3 + 5(2)^2 + 6(2) = 8 + 20 + 12 = 40
So....this one is false
Second one
x^3 + 5x^2 + 6x factor
x( x^2 + 5x + 6)
x(x + 3) ( x + 2)
So....this one is true
Third one
This is false...it will only have a remainder of 0 if divided by one of its factors....and (x - 2) is not a factor
Last one
f(-2) = 0 is true.....since ( x + 2) is a factor, - 2 is a root [ it will produce a 0 when plugged into the function and evaluated ]
