If we divide the polynomial x4 + 4x3 + 2x2 + x + 4 by x2 + 3x, what will be the remainder?

Answers

Answer 1

Answer:

$x^4+4x^3+2x^2+x+4 = Q(x)\cdot (x^2+3x)+ax+b,\;we\;need\;to\;find\;a,\;and\;b;\n\nx^4+4x^3+2x^2+x+4 = Q(x)\cdot x\cdot (x+3)+ax+b$

If you choose x = 0, then we have 4 = Q(0)*0 + a*0 + b, therefore b = 4.

If we choose x = -3, then we have:

$(-3)^4+4\cdot (-3)^3+2 \cdot (-3)^2-3+4 = Q(-3)\cdot (-3)\cdot (-3+3)-3a+4\Rightarrow 81-108+18+1=4-3a,\;or\;-12=-3a,\;so\;a=4.$

The remainder is: 4x+4.

Green eyes.

Related Questions

Write an expression that shows how to use the halving and doubling strategy to find 28 x 50
Perry observes the opposite , parallel walls of a room. In how many lines do the planes containing the walls intersect
find the minimum value of p=10x+26y the constraints are x+y less than or equal to 6, 5x+y greater than or equal to 10, x+5y greater than or equal to 14
In rectangle KLMN, KM = 10x+24 and KN = 64 find x
You are baking cupcakes for your class. There are 30 total students in your class and you have baked 15 cupcakes. Write andsolve an equation to find the additional number of cupcakes you need to bake in order to have 3 cupcakes for each student.Write your equation so that the units on each side of the equation are cupcakes per student.Equation:= 3Number of cupcakes: x=

Which best describes the range of the function f(x) = 2(3)x?y > 0

y ≥ 0

y > 2

y ≥ 2

Answers

The range of the function f(x) : $2.3^(x)$ is y > 0.

The correct option is (A)

What is range?

The definition of range is the set of all possible values that the function will give when we give in the domain as input.

Given function is : $2.3^(x)$

If we draw the graph for this, then we can see that the horizontal asymptote is 0.

So, the range is real numbers higher than 0.

Hence, the range should be y > 0.

Learn more about this concept here:

brainly.com/question/3952743

#SPJ2

The range of the function f(x) = 2(3)^x is y > 0

with no air resistance, an object would fall 16 feet during the first second, 48 feet during second second 80 feet during the third second, 112 feet during the fourth second, and so on, how many feet will be object fall during the ninth second

Answers

During the ninth second, the object will fall at 272 feet.

I need some help with this please! An explanation would be lovely too!

Answers

Answer:

Step-by-step explanation:

if m<ABC is = 40 and BD is besector then m<ABD = 20

Can someone solve this differentiation question.

Answers

We clearly see on the graph that :
A. f is increasing on (2,6) and (8,10) (the derivative is >=0)
B. f is decreasing on (0,2) and (6,8) (the derivative is <=0)
C. f has two relative minima : one at x=2 and one at x=8 (the derivative changes signs there from negative to positive)
D. f has two relative maxima : one at x=6 and one at x=10(the derivative changes signs there from positive to negative)
E. f is concave up when f' is increasing i.e. on (0,4) and (7,9)
F. f is concave down when f' is decreasing i.e. on (4,7) and (9,10)
G. the points of inflexion of f are the points at which f' has an horizontal tangent, thus they are at x=4, x=7 and x=9
H. see the picture attached

A). The function is increasing where its derivative is positive.
Its derivative is positive from 2 to 6, and from 8 to 10.

B). The function is decreasing where its derivative is negative.
Its derivative is negative from 0 to 2, and from 6 to 8.

C). The function has a relative minimum where its derivative is zero
and changing from negative to positive.
Its derivative is zero and changing from negative to positive at 2 and 8.

D). The function has a relative maximum where its derivative is zero
and changing from positive to negative.
Its derivative is zero and changing from positive to negative at 6 and 10.

E). The function is concave up between consecutive relative maxima.
The interval between consecutive relative maxima is 6 < x < 10 .

F). The function is concave down between consecutive relative minima.
The interval between consecutive relative minima is 2< x < 8 .

G). The function has points of inflection where its second derivative is
zero, that is, where its first derivative is a relative minimum or a relative
maximum.
Its first derivative is a relative minimum or maximum at x = 0, 4, 7, and 9 .

H). Good luck on the sketch !

The city park shown at the right has an area of 6889 m². The parks length along the front Street is 83 m. Find the length of the park along second Avenue.

Answers

length times width = area
83 m times w =6889
divide both sides by 83
and the second length w is 83m

Iliana’s math grade increased from 65 to 86. Fiona’s math grade increased from 70 to 80. What is the difference, rounded to the nearest whole number, between the approximate percent increases?

Answers

Iliana's math grade increased by 21 which is 32.31%. Fiona's math grade increased by 10 which is 14.29%. To obtain the difference between the percent increases, subtract 14.29 from 32.31. Thus, the difference in percent increases of their math grades is approximately 18%.

Answer:

18%

Step-by-step explanation:

Other Questions

Brandie lives on the twelfth floor of her apartment building. She walks down 2 flights to visit a friend, then up 3 flights to deliver a message to a neighbor. Which integer best represents the number of flights Brandie must walk to get back to her starting point?A.–12 B.–1 C.5 D.7

Alaina's sugar cookie recipe calls for 2 1/4 cups of flower. If she wants to make 2/3 a batch of cookies how much flour should she use?

The common stock of air united had annual returns of 13.7 percent, 4.8 percent, -6.7 percent, and 27.9 percent over the last four years, respectively. what is the standard deviation of these returns?

Which problem is being modeled on the number line?