Without actual division, prove that 2x^4 - 5x^3 + 2x^2 - x + 2 is divisible by x^2 + 3x + 2.

Answers

Answer 1

Answer:

Thinking Process

(i) Firstly, determine the factors of quadratic polynomial by splitting middle term.

(ii) The two different values of zeroes put in bioquadratic polynomial.

(iii) In both the case if remainder is zero, then bioquadratic polynomial is divisible by

quadratic polynomial.

Answer 2

Answer:

2x⁴ - 5x³ + 2x² - x + 2=

2x²(x²-3x+2) +x³-2x² -x +2=

2x²(x²-3x+2) + x(x²-3x+2) +x² -3x +2=

(x²-3x+2)(2x²+x+1)

since x²-3x+2 is the factor of the given polynomial, we can state the polynomial is divisible by x²-3x+2

-------------

note: x²+3x+2 is not the factor of the given polynomial


Related Questions

Which graph has a correlation coefficient, r, closest to 0.75?

Answers

Answer:

option A

Step-by-step explanation:

to find the correlation coefficient by hand, first put your data pairs into a table....

Graph C indicates the graph which has a correlation coefficient, r, closest to 0.75.

What is Correlation Coefficient?

Correlation coefficient of a data is the measure which indicates the strength of the linear relationship among two variables in a scatterplot.

Given are four graphs.

The range of values for correlation coefficient, r is from -1 to 1.

The value closest to -1 is considered weak linear relationship between the variables and value closest to 1 considered strong linear relationship between the variables.

Here the value of r is closest to 0.75.

Since it is closest to 1, the linear relationship is stronger. This means that the data points are more centered to form a line or they are close to each other.

Two such graphs are B and C.

Since r is 0.75, it is positive, So the relationship is positive.

So graph C is the correct one.

Hence graph C is the required graph.

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What is the value of x ?

Answers

Answer:

x=22

Step-by-step explanation:

set all of your values equal to 360 (bc thats the value of the degrees in a circle) and then solve for x!

75 + 92 + ( x+57 ) + ( x+92) = 360

( x+57 ) + ( x+92 ) = 201

2 x = 44

x = 22

Please please please help !!!
Figure ABCD is reflected about the y-axis to obtain figure A′B′C′D′:

A coordinate plane is shown. Figure ABCD has vertices A at 2 comma 5, B at 1 comma 2, C at 3 comma 1, and D at 4 comma 5. Figure A prime B prime C prime D prime has vertices A prime at negative 2 comma 5, B prime at negative 1 comma 2, C prime at negative 3 comma 1, and D prime at negative 4 comma 5.
Which statement best describes the relationship between the two figures? (4 points)

A)Figure ABCD is similar to figure A′B′C′D′.
B)Figure ABCD is bigger than figure A′B′C′D′.
C)The measure of angle D is equal to the measure of angle A′.
D)The measure of angle D is equal to the measure of angle B′.

Answers

Answer:

A

Step-by-step explanation:

These shapes are not identical, because the angles and sides are mirrored, but much like a mirrored object, they are similar. Another way to explain it is when you look into a mirror what you are seeing is not what people see when they see you with their eyes, it's a REFLECTION!

The correct option is Option A: figure ABCD is similar to A′B′C′D′.

What is reflection?

Reflection is the translation of the figure about an axis or point so that the distance of the reflected figure from the axis is the same as the distance of the original figure from the axis.

When a point of coordinate (x,y) is reflected about the y-axis then the coordinate of the reflected point will be (-x,y).

In quadrilateral ABCD the coordinate of A is (2,5) and the coordinate of A' is (-2,5). Here the coordinate of y is unchanged and the x coordinate is changed negatively. So point A' is the reflection of point A.

In quadrilateral ABCD the coordinate of B is (1,2) and the coordinate of B' is (-1,2). Here the coordinate of y is unchanged and the x coordinate is changed negatively. So point B' is the reflection of point B.

In quadrilateral ABCD the coordinate of C is (3,1) and the coordinate of C' is (-3,1). Here the coordinate of y is unchanged and the x coordinate is changed negatively. So point C' is the reflection of point C.

In quadrilateral ABCD the coordinate of D is (4,5) and the coordinate of D' is (-4,5). Here the coordinate of y is unchanged and the x coordinate is changed negatively. So point D' is the reflection of point D.

So all the points of quadrilateral ABCD are reflected about the y-axis.

As it is a reflection about the y-axis for which the size will not be changed and both the reflected and the original figure will be similar.

Therefore the correct option is Option A: figure ABCD is similar to A′B′C′D′.

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I don't understand this math problem need help plz!

Answers

Answer:

A' (-4, - 7), B' (-5, -4), C' (-4, -3), D' (-3, -4)

Step-by-step explanation:

When rotating about the origin at an angle of 90° in the counterclockwise direction, the given values of (x, y) are interchanged with y also taking a negative sign. That is ;

(x, y) - - - -> (-y, x)

Therefore, in the question above ;

Translation = (x-2, y+3)

A =(-5, 1) = (-5 - 2, 1 + 3) = (-7, 4) - - -> A' = (-4, - 7)

B =(-2, 2) = (-2 - 2, 2 + 3) =(-4, 5) - - -> B' = (-5, -4)

C =(-1, 1) = (-1 - 2, 1 + 3) = (-3, 4) - - -> C' = (-4, -3)

D =(-2, 0) = (-2 - 2, 0+3) =(-4, 3) - - -> D' = (-3, -4)

The graph of a linear function is shown
Which word describes the slope of the line?
positive
negative
zero
undefined

Answers

Answer:

the answer is b

Step-by-step explanation:

plz give me a Brainliest

A word that describes the slope of the line is negative. The correct answer is option B.

What is a graph?

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data. It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

For this case the first thing you should know is that we have an equation of the form:

y = mx + b

Where,

m: The slope of the line

b: Cutting point with the vertical axis.

For this case, we observe that the values of y decrease when the values of x increase. Therefore, the function decreases.

This means that it is true that:

m < 0

Therefore, the slope of the line is negative.

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Which pair of angles are vertical angles?

Answers

Answer:

angles 1 and 4, and angles 2 and 3

Answer:

1 and 4, 2 and 3

Step-by-step explanation:

Does this actually seem difficult? If you're in High school, because i'm in Middle school and I can answer this question.

what the answar for 9+4t=7t+15

Answers

Answer:

t= -2

Step-by-step explanation:

9+4t=7t+15

Subtract 4t from both sides

9=3t+15

Subtract 15 from both sides

-6=3t

3t= -6

Divide both sides by 3

t= -2

find the permimter of the quadrilateral if x=2 the perimiter is in inches the perimiters are (4x2+8x) (31 ) (7x+30) (3x2-5x+20)

Answers

Answer:

115

Step-by-step explanation:

4*2+8(2) = 24

31

7(2)+30 = 44

3*2-5(2)+20 = 6-10+20 = -4+20 = 16

24+31+44+16

115      

7(2) + 30 = 14+30 = 44
3(2^2) -5(2)+20 = 12 - 10 + 20 = 22
4(2^2) +8(2) = 16 + 16 = 32

P = 31 + 44 + 22 + 32 = 129

The perimeter is 129 inches

A fair dice is rolled.
Work out the probability of getting a factor of 8.
Give your answer in its simplest form.

Answers

Answer:

1/2

Step-by-step explanation:

The factors of 8 are 1,2,4

So there are three factors of 8 on the dice

There are a total of 6 numbers on the dice

So the probability is ,3/6

Which in its simplest form is 1/2

Solve:2/3 - 4x +7-2= -9.x +5/6
x = -3/2
x = -2/3
X=2/3
X=3/2

Answers

Answer:

2/3-4x+7-2=-9.x+5/6

2/3+7/1-2/1-5/6=-9.x+4x

12+126-36-15/18=-5x

87/18=-5x

29/6=-5x

29/6÷5=-5x÷5

29/6*1/5=-5x÷5

29/30=-x

-29/30=x

-0.9667=x

A red light
flashes on
every
8 secs and a
green light flashes on
flashes on every 10 secs. If the two
lights are switched on
at the same time.
After how long will both lights flash on
together?

Answers

Answer:

Both lights would flash together after every 30 seconds.

Step-by-step explanation:

6 = 2 * 3 and 10 = 2 * 5.

LCM (Least Common Multiple) of 6 and 10 = 2 * 3 * 5 = 30.

Therefore, both lights wold flash together after every 30 seconds.

Answer:

every 30 seconds.

Step-by-step explanation:

I'm a banana

I'm a banana

I'm a banana

Look at me move, yeah yeah

I'm a banana

I'm a banana

I'm a banana

Look at me move, ah

Banana power

Banana power

Banana power

Power

Banana power

Banana power

Banana power

Look at me move

Uh oh banana time

Uh oh banana time

Uh oh banana time

Stop

Stop

Stop

Carts, farts, marts, darts

Hearts, starts, carts, marts

Carts, marts, darts, farts

Darts, starts, hearts, ah

Chicken, chicken, chicken

I am

Chicken, chicken

Chicken

Stop

Look at me

Look at me move

I'm a banana

I'm a banana

I'm a banana

yes

2 shapes A and B, are similar.
length of edges in A : length of edges in B = 2.5
The perimeter of A is 210mm
work out the perimeter of B

Answers

Answer:

525 mm

Step-by-step explanation:

The edges of A : B = 2.5, thus

The perimeters of A : B = 2.5

Thus the perimeter of B is 2.5 times the perimeter of A

perimeter of B = 2.5 × 210 mm = 525 mm

Aramis showed the division of 6p2 + 9p + 3 by 3p. A + 3 + B What are the values of A and B? A = 2p and B = p A = 3p and B = p A = and B = A = 2p and B =

Answers

Answer:

D) A = 2p and B = 1/p

Step-by-step explanation:

To divide this,

we first see how many times 3p will go into 6p².

 [tex]\frac{6p^2}{3p} = 2p[/tex]

It will go in 2p times; this goes up top of the problem.

Multiplying back through, we have

[tex]2p*3p = 6p^2[/tex]

Subtracting this from the first term under the box, we have

[tex]6p^2-6p^2= 0.[/tex]

 This cancels.  Bring down the next term, 9p.

See how many times 3p goes into 9p = [tex]\frac{9p}{3p}=3[/tex]

it goes in 3 times.  This goes up top, beside the 2p.  We separate them with a +, since the 3 is positive.

Multiplying back through, we have 3(3p) = 9p.  

Subtract this from the line above; 9p-9p = 0.  

Bring down the last term, 3.  

Since this is not 0, this is the remainder.  

This gives us

2p + 3 R 3;

writing this as a rational expression, we have

[tex]2p + 3 + \frac{3}{3p}[/tex]

The remainder term, [tex]\frac{3}{3p}[/tex], will simplify to 1/1p or 1/p;

this gives us

[tex]2p + 3 + \frac{1}{p}[/tex]

Therefore, the answer is  A = 2p and B = 1/p

Answer:

D) A = 2p and B = 1/p

Step-by-step explanation:


Which is not a characteristic of the linear parent function?
A. It goes through the origin.
B. The domain is all real numbers.
C. It has a slope of 1.
D. The range is positive real numbers (y > 0).​

Answers

Answer: D

Step-by-step explanation:

4. In parallelogram PQRS, QP is extended to point T and ST is drawn. If ST SP and
m 130°
80°
65°
50°

Answers

In parallelogram PQRS, QP is extended to point T and ST is drawn. If ST = SP and m∠R = 130°, what is m∠PST?

Answer: 80°

Step-by-step explanation:

ST = SP and m∠R = 130°

If m∠R = 130°, then,

QPS = 130° ( Opposite angles of a parallelogram are equal)

QPS + SPT = 180° (angle on a staght line)

130° + SPT = 180°

SPT = 180° - 130° = 50°

PTS = SPT = 50° (Base Angle of an isosceles triangle)

m∠PST = 180° - (50° + 50°) (sum of Angle in a triangle)

m∠PST = 80°

Jaylen and Michael are making a pizza with a 16 inch diameter. They want to put three cheese blend on 5 of the 45° slices (including the crusts). Each handful of cheese covers 21 square inches, Calculate the area of the pizza slices that they want to put cheese on.

Answers

Answer:

125.66 in2

Step-by-step explanation:

The area of the pizza is given by the formula:

Area = pi * radius^2

The radius of the pizza is half the diameter, so radius = 16/2 = 8 inches

Then, the total area is:

Area = pi * 8^2 = 64pi in2

They will put cheese in 5 of the 45° slices, so the total angle covered is 5 * 45° = 225°.

If the full area of the pizza is 360°, we can find the area covered by cheese using a rule of three:

360° -> 64pi in2

225° -> x in2

x = (225/360) * 64pi

x = 125.66 in2

Please help! Correct answer only!

A raffle has 1,000 tickets. One ticket will win a $830 prize. The remaining tickets will win nothing. If you have a ticket, what is the expected payoff?

Answers

Answer:

" Expected Payoff " ⇒ $ 0.830

Step-by-step explanation:

Consider the probability of entering 1 ticket out of the 1000 entered;

[tex]Total Tickets Entered - 1000 Tickets,\\Prize Won - 830 Dollars,\\Number of Tickets One Can Enter - 1 Ticket,\\\\Probability of Winning - 1 / 1000,\\Proportionality - 1 / 1000 = x / 830, If x = " Expected Payoff ",\\\\1 / 1000 = x / 830 - Cross Multiplication ,\\1000 * x = 830,\\x = 830 / 1000 = 0.830\\\\Conclusion ; x = 0.83[/tex]

Solution ; " Expected Payoff " ⇒ $ 0.830 ( might or might not include 0 at end )

What does Arc CDE describe?

a minor Arc

a major Arc

a semicircle

a chord

Answers

Answer:

I believe it's major arc

Step-by-step explanation:

Second option on edge

Answer:

b

Step-by-step explanation:

Write 150 as a product of primes. Use index notation where appropriate.

Answers

Answer:

150=2x5x5x3, or 150=2x5^2x3

Step-by-step explanation:

150=50x3

50=5x10

10=2x5

150=2x5x5x3

The total cost of a new calculator is $81.05. This price includes a 10% discount followed by a 6.5% sales tax. What was the original price of the calculator not including the tax or the discount?

Answers

Answer:

68.245

Step-by-step explanation:

total cost = $81.05

10% discount is 10/100× 81.05=8.105

substract 8.105 from 81.05= 72.945

with a 6.5% sales tax

6.5/100× 72.954 = 4.7

72.945-4.7= 68.245 the actual price

if am wrong let me know

five more than a half number is 6. find the number.

Answers

First write the equation:
1/2x + 5 = 6

Then subtract five from both sides:

1/2x = 1

Multiply both sides by 2:

x = 2
Equation :
1/2x +5 = 6

Subtract both sides by five:
1/2x = 1

Multipy by 2:
X=2

Please answer correctly !!!!!!!! Will mark brianliest !!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

Since length times width = the area, you know that the area divided by the length is the width. This means that 6x^2 + 10 / 2 = the length.

6x^2 / 2 = 3x^2

10/2 = 5

You end up with 3x^2 + 5 as the length.

Answer & Step-by-step explanation:

Since you trying to find the width when you are given the length and the area, then you are going to divide the area by the length to get the width.

(6x² + 10) ÷ 2

We can also put this into a fraction so it will be easier to know what you are dividing.

[tex]\frac{6x^2+10}{2}[/tex]

Divide 6x² by 2 and divide 10 by 2. Keep the exponent because 2 does not have a variable.

So, your width will be 3x² + 5

What is the price called at which the quantity demanded is equal to the
quantity supplied?
Hola
Done
Clear
Ali

Answers

The answer is done or clear

A lock requires a 3 number combination using the numbers 0 through 9, none of which may be repeated. How many outcomes are possible?

48

720

12010




Answers

Answer:

720

Step-by-step explanation:

The lock requires that repetition is not allowed.

The possibles numbers are 0 - 9, that is, 10 digits.

The first number in the combination can be picked from the 10 digits.

This means that there are 10 possible choices.

The second number in the combination can now only be picked from 9 digits.

This means that there are 9 possible choices.

The third number in the combination can now only be picked from 8 digits.

This means that there are 8 possible choices.

Therefore, the number of possible outcomes in the combination is:

10 * 9 * 8 = 720 outcomes

What is the range of the function 2x + y = 7
if the domain is {-4, -2,0, 5, 7)?​

Answers

Answer| range: {15, 11, 7, -3, -7}

Step-by-step explanation:

Plug in the domain to find the range:

x = 4

2(-4) + y = 7

-8 + y = 7

y = 15

x = -2

2(-2) + y = 7

-4 + y = 7

y = 11

x = 0

2(0) + y = 7

0 + y = 7

y = 7

x = 5

2(5) + y = 7

10 + y = 7

y = -3

x = 7

2(7) + y = 7

14 + y = 7

y = -7

Simplify the following exponential expression.
14405c4
- 166c-14

Answers

ANSWER!
14405c•4-166c-14
57620c-166c-14
57454c-14
I hope this helps!

Solve the equation for y: x = 2y - 3

Answers

Answer:

[tex]y = \frac{1}{2} x+\frac{3}{2}[/tex]

Step-by-step explanation:

Select all the equations where y=10equals, is a solution.
Choose 2 answers:



A
y+11=22


B
8=18-y


C
60=6y


D
y/5=4

E
10y=20

Answers

Answer:

B and C

Step-by-step explanation:

A. y + 11 = 22         →  subtract 11 from both sides:

    y = 11

---------------------------------------------------------------------------

B. 8 = 18 - y           →  subtract 18 from both sides:

    -10 = -y              →  divide both sides by -1:

     10 = y

----------------------------------------------------------------------------

C. 60 = 6y             →  divide both sides by 6:

    10 = y

-----------------------------------------------------------------------------

D. [tex]\frac{y}{5}[/tex] = 4                  →  multiply both sides by 5:

   y = 20

-----------------------------------------------------------------------------

E. 10y = 20            →  divide both sides by 10:

     y = 2

Please help! select the correct answer

Answers

Answer:

the answer is show me your kitty cat

Step-by-step explanation:

Simplify the expression:
6b – 2b+ 5b – 8

Answers

Answer:

9b-8

Step-by-step explanation:

6b+5b-2b-8

11b-2b-8

9b-8

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