How to synthetically divide polynomials.

Answers

Answer 1

Answer:

Write down the problem. For this example, you will be dividing x3 + 2x2 - 4x + 8 by x + 2. Write the first polynomial equation, the dividend, in the numerator and write the second equation, the divisor, in the denominator.

Reverse the sign of the constant in the divisor. The constant in the divisor, x + 2, is positive 2, so reversing the sign of the constant would give you -2.

Since the opposite of the constant term is -2, we put the -2 inside a box. A common mistake is to put a 2 inside the box, watch out here.

Write all of the coefficients of the dividend inside the division symbol. [2] Write the terms from left to right, just as they appear. It should look like this: -2| 1 2 -4 8.

Bring down the first coefficient. Bring down the first coefficient, 1, below itself. It should look like this:

-2| 1  2  -4  8

   ↓

   1

Multiply the first coefficient by the divisor and place it under the second coefficient.[3] Simply multiply 1 by -2 to get -2 and write this product under the second term, 2. Here's how it would look:

-2| 1  2  -4  8

       -2

   1

Add the second coefficient and the product and write the answer below the product. Now take the second coefficient, 2, and add it to -2. The result is 0. Write this result below the two numbers, just as you would in long division. Here's how it would look:

-2| 1  2  -4  8

       -2

   1   0

Multiply this sum by the divisor and place the result under the third coefficient. Now take the sum, 0, and multiply it by the divisor, -2. The result is 0. Place this number below 4, the third coefficient. It should look like this:

-2| 1  2  -4  8

       -2  0  

   1  

Add the product and the third coefficient and write the result under the product. Add 0 and -4 to get -4 and write this answer below the 0. Here's how it would look:

-2| 1  2  -4  8

       -2   0  

   1   0   -4

Multiply this number by the divisor, write it under the last coefficient, and add it to the coefficient. Now, multiply -4 by -2 to get 8, write this answer under the fourth coefficient, 8, and add this answer to the fourth coefficient. 8 + 8 = 16, so this is your remainder. Write this number below the product. Here's how it would look:

-2| 1  2  -4  8

       -2   0   8

   1   0   -4   |16

Place each of the new coefficients next to a variable of one less power than their original corresponding variables. In this case, the first sum, 1, is placed next to an x to the second power (one less than three). The second sum, 0, is placed next to an x, but the result is zero, so you can remove this term. And the third coefficient, -4, becomes a constant, a number without a variable, since the original variable was x. You can write an R next to the 16, because that is the remainder. Here's how it would look:

-2| 1  2  -4  8

       -2   0   8

   1   0   -4   |16

   x2   + 0x    - 4    R 16

x2 - 4 R16

Write the final answer. The final answer is the new polynomial, x2 - 4, plus the remainder, 16, over the original divisor, x + 2. Here's how it would look: x2 - 4 +16/(x +2).

Step-by-step explanation:

That was quite long, but those are the steps to synthetically divide polynomials.


Related Questions

To form a hyperbola what is the relationship between the base of the cone and the angle of the plane that intersects the cone

A. The plane is a parallel to the base of the cone

B. The plane may be perpendicular to the base of the cone

C. the plane must be at a 45 degree angle to the base of the cone

D. The plane is at an angle that is neither parallel nor perpendicular to the base of the cone

Answers

It’s b, you’re welcome.

what are the four functions that are increasing on the interval

Answers

Answer:

Tbh i don’t really know

Step-by-step explanation:

Ask someone else

Identity function
Cubing function
Reciprocal function
Sine function

A pole 11 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Rashaad measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.

Answers

The given question is on trigonometry which requires the application of required function so as to determine the value known. So that the length of the guy wire is 67.0 feet.

Trigonometry is an aspect of mathematics that requires the application of some functions to determine the value of an unknown quantity.

Let the length of the guy wire be represented by l, and the angle that the guy wire makes with the stake be θ. So that applying the appropriate trigonometric function to determine the value of θ, we have:

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

          = [tex]\frac{11}{4}[/tex]

Tan θ = 2.75

θ = [tex]Tan^{-1}[/tex] 2.75

  = 70.0169

θ = [tex]70^{o}[/tex]

Considering triangle formed by the tower and the stake to determine the value of l, we have;

Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]

Cos [tex]70^{o}[/tex]  = [tex]\frac{23}{l}[/tex]

l = [tex]\frac{23}{Cos 70^{o} }[/tex]

 = [tex]\frac{23}{0.3420}[/tex]

l = 67.2515

l = 67 feet

The length of the guy wire is 67 feet.

For more on trigonometric, check: https://brainly.com/question/6459892

solve for q
q/-2+17=13

q=

Answers

Answer:

q = 8

Step-by-step explanation:

-q/2 + 17 = 13

subtract 17 from each side to get:

-q/2 = -4

to isolate the 'q', multiply each side by -2 to get:

q = 8

Solve for x then y.
y+10=-1/6(x-6)

Answers

Answer:

y= -x/6-9

x= -6y-54

Step-by-step explanation:

someone help me pls
i need it now
just simply choose the letter of the correct answer​

Answers

Answer:

Step-by-step explanation:

1. D

2. A

3. A

4. B

5. B

dont know the rest sorry

which of the following is not a true dilation?

A. The image and preimage have congruent angles

B. The image and preimage have proportional sides

C. The image and preimage are congruent

D. The image and preimage are similar

Answers

Answer:

umm i think it is B.

Step-by-step explanation:

Select all statements that are true about the triangles.

Figure ABCD with diagonal BC, sides AB and DC are congruent, angle A is congruent to angle D and sides AC and DB are congruent.
Group of answer choices

Triangles ABC and BCD are congruent by the Angle-Side-Angle Triangle Congruence Theorem.

Triangles ABC and DCB are congruent by the Angle-Angle Triangle Congruence Theorem.

Triangles ABC and DCB are congruent by the Side-Side-Side Triangle Congruence Theorem.

Triangles ABC and DCB are congruent by the Side-Angle-Side Triangle Congruence Theorem.

Triangles ABC and BCD are congruent by the Side-Side-Side Triangle Congruence Theorem.

There is not enough information to determine if the triangles are congruent

Answers

Answer:

Triangle ABC and BCD are congruent by the side side side triangle congruence theorem

Pls help me i only have 20 mins

Answers

Answer:

In bold below.

Step-by-step explanation:

Part 1A: 60 hours * $11.50.

Ashly's GMI is $690.00

Part 2A: To find out how much Ashly's income goes towards technology, we need to find out how much 10% of $690.00 is. To do that, multiply 690 * 0.1. You'll get $69.00.

$69.00 goes towards Ashly's technology.

Part 2B: To find out how much she spends on lunch, we must do the same as above, only replacing 0.1 with 0.02. 690.00 * 0.02 = 13.8

$13.80 goes towards Ashly's technology.

Part 2C: $13.80 + $69.00 = $82.80

$82.80 is Ashly's monthly deductions.

Part 3A: If Ashly's annual salary is $8,280, we divide that by 12 to see how much she gets per month.

 Ashly's GMI is $690.00

When resting, a spring measures 73.3 millimeters. When the spring is
compressed, it measures 51.29 millimeters. Find the percent of
decrease in the length of the spring. Round to the nearest percent if
necessary

Answers

Answer:

  -30%

Step-by-step explanation:

The percentage change in length is given by ...

  percent change = ((new length) -(original length))/(original length) × 100%

  = (51.29 -73.3)/73.3 × 100%

  = -22.01/73.3 × 100% = -0.30027 × 100%

  = -30%

The decrease in the length of the spring was 30%.

Answer:

30

Step-by-step explanation:

because divide

A shop increases all its prices by 10%. Calculate the new price for an article which was previously sold for £7,500

Answers

Answer:

Your answer is 8250

Step-by-step explanation:

STEPS:

7500 x (1+0.1)

7500x1.1 = 8250

Hope this helped :)

PLS HELP WILL MARK BRAINLIEST!

Answers

Answer:

I think the answer is B.

Step-by-step explanation:

Answer:

c. 81x^2 -4y^2

Step-by-step explanation:

Area of full square - area of white square.

Lines A and B have
the same y-intercept,
but different slopes.
Both slopes are
negative.

PARALLEL PERPENDICULAR OR NEITHER

Answers

Answer:

Neither

Step-by-step explanation:

Since line a and b have different slope, it isnt parallel, and since the slopes both negative, its not an opposite reciprocal, so that isnt perpendicular, thus leading to neither

The table gives information about the heights of 50 trees. Work out an estimate for the mean height of the trees.

Answers

Answer:

add h then divide by 2 for h times f

Step-by-step explanation:

The circumference of a circle is 20pi m. find its diameter,in meters

Answers

Answer:

20 m

Step-by-step explanation:

Circumference formula:

C = πd

Substitute and solve for d:

20π = πdd = 20π/πd = 20

Someone please help me. Thank you!

Answers

Answer:

y = -1/2x

Step-by-step explanation:

Okay, so you probably heard of the slope-intercept form, y = mx + b. We have to use that formula to create a line that goes through (2,1), because thats the bisector.

Let's have our point start at the origin, (0,0). This you make our equation of y=mx+b   into   y = mx + 0. Since it's 0, let's just drop it out of our equation.

So now for slope. Rise/Run is what we're going to use to create our slope. Since we started at the origin, our slope is going to be negative. We can go down one over two from the origin to get to points (2,1) so why can't that be our slope? We're rising -1, and running 2, making our slope -1/2. In the equation, it would be y= -1/2x + 0, which can be simplified into y = -1/2x

It's a lot of writing and explaining, so I hope this helps! Try asking your teacher just to make sure it's correct.

Select all the rates equivalent to the rate 3/4 cup per pound

Answers

Answer:

Step-by-step explanation:

Multiply the decimal by 100 and write the result with the percentage sign: 0.75 × 100 = 75%.

variables combining like terms
16. x+3
17. 5y+3
18. x+5y-5

Answers

Answer:

16.3x

17. 8y

18.x+y

I thing these are the answers of these equations

x + 3 is not the same as 3x

please help!! this is for my geometry class

Answers

Answer:

x = 48°

Step-by-step explanation:

The triangle on the left has 3 congruent sides and is equilateral with 3 congruent angles, each of 60°

The 3 angles on the base line sum to 180° , that is

60° + 54° + base = 180°

114° + base = 180° ( subtract 114° from both sides )

base = 66°

The triangle  on the right has 2 congruent sides and is isosceles with base angles congruent , both 66° , then

x = 180° - (66 + 66)° = 180° - 132° = 48°

I need help pls help me

Answers

Answer:

$1,270

Step-by-step explanation:

let x be the total amount of ice cream sold without tax

x + (x*0.0635)=21270

1.0635x=21270

x=20,000

so the amount he needs to send to state is

21270-20000

1,270

Total cost of icecream without cost be x

[tex]\\ \sf\longmapsto x+0.0635x=21270[/tex]

[tex]\\ \sf\longmapsto 1.0635x=21270[/tex]

[tex]\\ \sf\longmapsto x=21270/1.0635=20000[/tex]

Amount to be paid

[tex]\\ \sf\longmapsto 21270-20000=1270[/tex]

If the radius of a circle equals 20 cm find its circumference correct to one decimal place

Answers

Answer:

125.66

Step-by-step explanation:

i don't get the one decimal place part but there your answer

The answer is 125.7 correct to one decimal place

Find the measure of each angle indicated.

Answers

Step-by-step explanation:

92°

as the has given pair of angle is Alternate Exterior angle so they have same values.

HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE

HELP ASAP

Solve for the measure of ∠PMR

Answers

Answer:

116*

Step-by-step explanation:

Since <PMR consists of <RPW and <WPM and we know that these are the same, we just have to multiply 58 by 2 and get 116, which will be your answer.

Tell me if I'm wrong :)

HELLLP-
What is the location of the origin?
(0,0)
(1,1)
0
(10,10)

Answers

The origin is where the y axis and x axis meet which is (0,0)

What’s the product of 2.6

Answers

Answer:

2×6=12

Step-by-step explanation:

Please help homework due tomorrow!!

12. Ms. Kerr needs $450 to purchase new volleyballs. She has already saved 65% of the money, how much
additional money does she need to save to have enough to purchase the equipment?

13. A 6th grade student is 5 feet tall and casts a 12 foot shadow. How tall is the 8th grader standing next to
him that casts a 14.4 foot shadow?

Answers

Answer:

12-157.5  13-6ft

Step-by-step explanation:

the first one just look up 65% of 450 and minus the number you get by 450

the second one do the butterfly method

[tex]\frac{5}{12} \frac{x}{14.4} \\[/tex]

the heights on top and shadows on bottom

12x=72

x=6

1. 1. MP.5 Use Appropriate Tools Carla had a piece of rope that was 14 in. long. She used some of the rope for a crafts project. Now there is 14 in. left. How much rope did she use? Use the number line to help.​

Answers

Answer:

4/8, 1/2

Step-by-step explanation:

7/8 - 3/8 = 4/8

4/8 >>> divide both by 4

4 divided by 4 = 1

8 divided by 4= 2

1/2 Inches

Find the missing dimensions: Use the scale factor 1/4:3

Answers

Answer:

The answer is 1/4!

Step-by-step explanation:

I believe it’s 1/4 I’m not sure sorry if I’m wrong

If there are four quarts in a gallon, how many quarts are in 101/2 gallons?

Answers

Answer:

202

Step-by-step explanation:

What is 5/6 of 78kg?

Answers

65 kg i think or 143 pounds
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