# f(x) = x^4 - 6x^3 - 40x + 33 Use synthetic division and the Remainder Theorem to find f(-2) =  ________  , f(7) = ________

aruv | Student

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

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|  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

aruv | Student

`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.