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

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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 .

step-by-step explanation: h: (- 3, 6)

m: (1, - 2)

o: (7, 6)

r: (- 9, - 2)

midpoint of hm: (- 1, 2)

midpoint of or: (- 1, 2)

therefore, b is the midpoint of both diagonals bisect each other !

to prove the diagonals are perpendicular, show that the product of the slopes = - 1

both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph