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

Guest Nov 2, 2018

#1**+1 **

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 ]

CPhill
Nov 2, 2018