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4. Which of the following binomials is a factor of the quadratic 4x^2 - 35x + 24? Try to do this without factoring but by using the Remainder Theorem.

 

(1) x + 6

 

(2) x - 4

 

(3) x - 8

 

(4) x + 2

 

5. Which of the following linear expressions is a factor of the cubic polynomial x^3 + 9x^2 + 16x - 12?

 

(1) x + 6

 

(2) x - 1

 

(3) x - 3

 

(4) x + 2

 Feb 10, 2019
 #1
avatar+101856 
+2

Here's how to do the first one, GM

 

Evaluate    - 6 , 4, 8  and - 2   in the polynomial   [ one at a time, of course ]

 

Whichever gives you a 0   [ maybe more than one ]  will be the answer(s)

 

For example....if we put -6 into the polynomial and get 0,  then  [ x - (-6)  ]    = x + 6  will be an answer

 

If you have any questions.....let me know....

 

 

cool cool cool

 Feb 10, 2019
 #2
avatar+101856 
+2

5. Is done similarly

 

Remember that if  x - a is a factor.....then a is a root.....in other words...P(a) will equal 0

 

So....for x + 6     we can write   [ x - (-6) ]

 

And   "a" =  - 6

 

So....put -6 into the polynomial....if you get 0,  then x + 6 is a factor

 

Do the same thing for  (2)  (3) and (4)

 

If you are confused....let me know....this IS a little tricky  !!!!

 

 

cool cool cool

 Feb 10, 2019

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