Write the function in the form f(x) = (x - k)q(x) + r for the given value of k.

Question

f(x) =x^3+5x^2-3x-21, k=(squareroot of)3

Answer 1

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Answer 2

q(x) is the quotient when you divide f(x) by (x-√3).  r is the remainder when using division.

 

 

Using synthetic division,

 

√3  |   1             5                 -3                          -21

 

                       √3              (3+5√3)                     15

___________________________________________________

          1        (5+√3)              5√3                         -6

 

 

 

 

q(x) = x² + (5 + √3)x + 5√3

 

r = -6

 

 

Now just plug this into the form.

Answer 3

f(x) = x³ + 5x² - 3x - 21

Using synthetic division

 

√3   1    5           -3         -21

            √3     5√3 +3       5

        1 5+√3      5√3        -16

 

f(x) = (x - √3)[(x² + (5+√3)x + 5√3] -16