Express f(x) in the form f(x) = (x - k)q(x)+r for the given value of k. f(x)= x^3+ 4x² + 5x + 2, k= -2

Given:

To find:

The the given function in the form .

Solution:

We have,

The coefficients of f(x) are 1, 4, 5, 2.

Divide the given function by (x+2) by using synthetic division as shown below:

-2 | 1        4           5         2

              -2         -4        -2

_____________________

      1        2          1           0

_____________________

Bottom row represent the quotient and last element of the bottom row is the remainder.

Degree of the function is 3 and the degree of division is 1. So, the degree of the quotient is 3-1 = 2.

So, the quotient is and the remainder is 0.

Now,

Here, q(x) is the quotient and r is the remainder.

Therefore, the required answer is .

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step-by-step explanation:

do it yourself, cause that made me do it myself today, in english!