We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
-5
300
5
avatar+16 

6. Consider the cubic polynomial p(x) = x^3 + x^2 - 46x + 80.

 

(a) Using polynomial long division, write the ratio of p(x)/(x-3) in quotient-remainder form, i.e. in the form q(x) + (r)/(x-3). Evaluate p(3). How does this help you check your quotient-remainder form?

 Feb 10, 2019
 #1
avatar+19797 
+3

 

                  x^2+4x-34       -  22/(x-3)

x-3  |  x^3+x^2-46x+80

          x^3 -3x^2

        _______________

                  4x^2-46x

                  4x^2-12x

                _____________

                          -34x+80

                          -34x+102

                           __________

                (remainder)  -22

 

Basically with remainder  -22/(x-3)     then  p(3)  will equal -22

 

See cphill's explanation/answer here for the second part:

https://web2.0calc.com/questions/what-does-this-mean_10

 Feb 10, 2019
edited by Guest  Feb 10, 2019
edited by ElectricPavlov  Feb 10, 2019
 #2
avatar+104723 
+2

Using EP's answer of R = -22

 

We should get the same answer by subbing 3 inito the polynomial....so...

 

(3)^3 + (3)^2 - 46(3) + 80 =

 

27 + 9 -  138 + 80 =

 

116 - 138 =

 

-22       ......Magic !!!!!

 

 

cool cool cool

 Feb 10, 2019
 #3
avatar+16 
-3

Wait... I don't understand by the question: How does this help you check your quotient-remainder form?

 Feb 10, 2019
 #4
avatar+104723 
+1

It helps because     the    "r"  in   r / [ x - 3 ]     should be the same as evaluating P(a)

 

So...in the case EP divided the polynomial by x - a  =  x - 3        got  a remainder of -22

 

Then....we can check whether this remainder is correct by evaluating P(a) = P(3)

 

Note that when we evaluated P(3)....we put 3 into the polynomial and got -22

 

So....we can be sure that this remainder is correct....!!!!!

 

Does that make sense, GM???

 

 

cool cool  cool

CPhill  Feb 10, 2019
edited by CPhill  Feb 10, 2019
 #5
avatar+16 
-3

Ahh...Everything makes perfect sense now! Thanks a lot!

 

--Mr. SHADOW

GAMEMASTERX40  Feb 10, 2019

36 Online Users

avatar
avatar