+0  
 
+2
66
5
avatar+1786 

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+17331 
+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+98130 
+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+1786 
0

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

 Feb 10, 2019
 #4
avatar+98130 
+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+1786 
+1

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

 

--Mr. SHADOW

GAMEMASTERX40  Feb 10, 2019

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