+0  
 
0
43
3
avatar+67 

 

Given  5x^3+8x^2−7x−6

1) The binomial (x+2) is a factor of the polynomial expression. Describe how you know it is a factor.

2) The binomial (x+1) is NOT a factor of the polynomial expression. Explain how you know it is not a factor.

skye25  Oct 25, 2018
 #1
avatar+90969 
+2

 5x^3+8x^2−7x−6

 

If   (x + 2)  is a factor then  -2   must be a root

So...putting  -2  into   5x^3+8x^2−7x−6  and evaluating we get

 

5(-2)^3  + 8(-2)^2   - 7(-2)  - 6   =

 

-40  +  32     +  14   - 6    =

 

-8    +  8    =   0

 

We get a 0....this tells us that -2 is a root and ( x - -2)  = (x + 2)  is a factor

 

 

If  x + 1 is a factor....then -1 must be a root

 

So

 

5(-1)^3  + 8(-1)^2   - 7(-1)  - 6  =

 

-5    +  8   +   7    - 6  =

 

3   +  1    =

 

4

 

This does not produce a  0...so......-1 isn't a root and  ( x - - 1)   = ( x + 1)  isn't a factor  !!!

 

 

 

cool cool cool

CPhill  Oct 25, 2018
 #2
avatar+67 
+2

thank you

skye25  Oct 25, 2018
 #3
avatar+90969 
+2

No prob, skye  !!!!

 

 

 

cool cool cool

CPhill  Oct 25, 2018

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