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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

 Nov 2, 2018
 #1
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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  ]

 

 

cool cool cool

 Nov 2, 2018
 #2
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0

Thank you so much! can you answer one more question for me?

 Nov 2, 2018
 #3
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0

Factor the polynomial function over the complex numbers.

 

f(x)=x4−x3−2x−4

 

Enter your answer in the box.

f(x) = 

 

(in this question the answer probably have the symbol i in it)

 Nov 2, 2018

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