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:

[tex]f(x)=x^3+4x^2+5x+2,k=-2[/tex]

To find:

The the given function in the form [tex]f(x)=(x-k)q(x)+r[/tex].

Solution:

We have,

[tex]f(x)=x^3+4x^2+5x+2[/tex]

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 [tex]x^2+2x+1[/tex] and the remainder is 0.

Now,

[tex]f(x)=(x-k)q(x)+r[/tex]

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

[tex]f(x)=(x-k)(x^2+2x+1)+0[/tex]

Therefore, the required answer is [tex]f(x)=(x-k)(x^2+2x+1)+0[/tex].

Freddy read 50% of his book. Express this percent as a fraction in simplest form and as a decimal.
Fraction:
Decimal:

after spending 7/9 of a three hours examination, a student left the exams hall. How many minutes has he to complete the duration of the examination.​

reduce 105 in the ratio 3:5​

A television game show has 10 doors, of which the contestant must pick 2. Behind 2 of the doors are expensive cars, and behind the other 8 doors are consolation prizes. The contestant gets to keep the items behind the 2 doors she selects. Determine the probability that the contestant wins no cars. The probability is (Type an integer or a simplified fraction.)​

In the relationship between hours driven and distance traveled is y = 45x, which of the following ordered pairs would be graphed on the line that represents the relationship?

The ages of attendees at two different movies were randomly sampled. The data is in the double box plot. Drag each statement to the table to show whether it applies to Movie A or movie B

Is it possible for a cross section of a cylinder to have a triangular shape?

What’s 2+2?

(Ik it’s easy I’m tryna help ya out w points)

Your answer need enthusiasm!

Example:

ALL CAPS

Exclamation points!!!!!

Repeat in words like: YES YES

Needs funny words like, GURL, I wOnDeR wHat, etc.

Be creative! It doesn’t have to be correct, but funny!

Omg please help me. ​

Which situation CANNOT be represented by the equation x + 18 = 52

A. Madison and JADA made 52 cupcakes for the school bake sale. Madison made 18 cupcakes. How many cupcakes x JADA make? B. Selena has 52$`to spend at the store. She brought a new shirt for 18$ and a new pair of shoes. HOw much x did the new shoes cost?
C. Andrea has to read 52 pages per week for homework. On Monday night she reads 18 pages. How many pages x does Andera still needs to read? D. Leiro has 52 baseball cards he also has 18 football cards. How many total card x does leiro has?

I need help with number 9

Using the line of bets fit, about how much would you expect a kitten to weigh at 11 weeks?

can somebody please help me out ?

Help! Everyone keeps trolling me!


Below is the graph of equation y=−|x−2|+2. Use this graph to find all values of x such that

1. y > 0

2. y < 0

3. y = 0


Please add a real answer!

Thx so much for helping!

What quadrant is (0,-7) found in?

what is the Estimate of 3583.37

Find the area and the circumference of a circle with diameter 6 yd Use the value 3.14 for n , and do not round your answers.

How much is Sam's 11% commission on $350,000 in sales?

Which function describes this table of values
Is it A or B or C or D

Zeke and Scarlett deposit $500.00 into a savings account which earns 5% interest
compounded annually. They want to use the money in the account to go on a trip in 3 years.
How much will they be able to spend?
= P 1 + , where A is the balance (final amount), P is the principal
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years.

The width of a rectangle is 2 3/8 inches. The rectangle is 1 3/4 inches longer than it is wide Find the Length of the rectangle and preimeter of the rectangle

3 1/4 pints =____ fl oz?

B. Evaluate
a) [ (-48) ÷ 12 ] ÷ 4
b) [ (-16) +6 ] ÷ [(-2) +1 ]
c) 0 ÷ (-15)​

Suppose a large labor union wishes to estimate the mean number of hours per month a union member is absent from work. The union decides to sammple 348 of its members at random and monitor the working time of each of them for 1 month. At the end of the month the total number of hours absent from work is recorded for each employee . if the mean and standard deviation of the sample are x = 7.5 hours and s = 3.5 hours, find a 99% confidence interval for the true mean number of hours a union member is absent per month. Round to the nearest thousandth.
A) 7.5 ± .258
B) 7.5 ± .186
C) 7.5 ± .026
D) 7.5 ± .483

1 1/4 x 1 1/3 plsss help

(8+2b)+(-4+6x)+(6+9m)

PLZ ANSWER, 8 POINTS

ok so i need help and fast!!!!!

(ALGEBRA 2) Please help me with this question. Image is attached ( Please don't answer if you don't know )

What is the area of a triangle that has a base of 15 yards and a height of 11 yards?
O 165 yd 2
41.25 yd 2
O 330 yd 2
O 82.5 yd 2
Please asap

The two figures are similar. Find the ratios
(red to blue) of the perimeters and of the
areas. Write the ratios as fractions in
simplest form.

(100 points)