Homework Help

f(x) = x^4 - 6x^3 - 40x + 33 Use synthetic division and the Remainder Theorem to find...

user profile pic

kristenmarieb... | Student, Grade 10 | Valedictorian

Posted July 23, 2013 at 3:31 AM via web

dislike 0 like

f(x) = x^4 - 6x^3 - 40x + 33

Use synthetic division and the Remainder Theorem to find

f(-2) =  ________  , f(7) = ________

Tagged with algebra2, math

2 Answers | Add Yours

user profile pic

aruv | High School Teacher | Valedictorian

Posted July 23, 2013 at 4:11 AM (Answer #1)

dislike 1 like

`f(x)=x^4-6x^3-40x+33`

`f(-2)=(-2)^4-6(-2)^3-40(-2)+33`

`=16+48+80+33=177`

`f(7)=7^4-6xx7^3-40xx7+33`

`=96`

Thus by remainder theorem ,when f(x) is divided by (x+2) and (x-7) respectively leaves remainder 177 and 96 respectively.

Synthetic division when divided by x+2

       |x^4     x^3      x^2      x      cons.                                        ------------------------------------------------                             -2  | 1       -6           0       -40        33                                   

       |          -2          16      -32       144                                       --------------------------------------------------                     |  1      -8           16      -72       177

Synthetic division when divided by x-7

       |x^4     x^3      x^2      x      cons.                                        ------------------------------------------------                              7 | 1       -6           0       -40        33                                   

       |           7           7         49       63                                       --------------------------------------------------                     |  1       1           7          9        96

The umbers written in bold is remainder.

user profile pic

aruv | High School Teacher | Valedictorian

Posted July 23, 2013 at 4:19 AM (Answer #2)

dislike 1 like

Sorry typographical error above.Please its appearance should be as

Synthetic division when divided by x+2

       |x^4     x^3      x^2      x      cons.  

---------------------------------------------

 -2  | 1       -6           0       -40        33     

      |          -2           16     -32       144

----------------------------------------------

      |  1       -8           16      -72      177

Synthetic division when divided by x-7

       |x^4     x^3      x^2      x      cons.  

---------------------------------------------

    7 | 1       -6           0       -40        33                                   

       |           7           7         49       63      

---------------------------------------------

       |  1       1           7          9        96

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes