Write the function in the form fx x kqx r for the given va

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

f(x) = x^3 + 2x^2 3x 14, k = sqrt(3)

Solution

x - k = x - sqrt (3)

x - sqrt (3) = 0

x = sqrt (3)

f(sqrt 3) = (sqrt 3) ^3 + 2( sqrt 3 ) ^2 3 ( sqrt 3) 14

= 3 sqrt ( 3) + 2 * 3 - 3 ( sqrt 3) 14

= 6 - 14

= - 8 = r

q(x) = (x^2 + x ( sqrt 3 + 2) + 2 sqrt 3)

the function in the form f(x) = (x k)q(x) + r is

f(x) = (x sqrt 3) (x^2 + x ( sqrt 3 + 2) + 2 sqrt 3) - 8