Answers
Answer:
The quotient when [tex]x^3-4x^2-8x+8[/tex] is divided by [tex]x+2[/tex] is [tex]x^2-6x+4[/tex] with no remainder, so x+2 is a factor of p(x).
Step-by-step explanation:
As the question suggests, there are two ways to solve this problem: long division (which can always be used to divide polynomials), and synthetic division (which can only be used when you are dividing by something of the form [tex](x-a)[/tex]. In this case, we may use synthetic division, since [tex]x+2[/tex] is equal to [tex]x-(-2)[/tex]. I will use synthetic division here as it is slightly faster than long division.
The -2 on the left represents that we are dividing by x-(-2), and the rest of the numbers in the top row are the coefficients of p(x): 1, -4, -8, and 8.
The first step in synthetic division is to being down the leading coefficient of the polynomial: in this case, the 1 (as indicated in red). Now, we multiply the 1 by -2. We get -2, which we place directly below the -4.
Next, we add directly down the column, (-4 + (-2) is equal to -6), and this answer is placed in the box below. We can continue this process, getting the coefficients 1, -6, 4, and 0 in the bottom row.
This is the answer: the quotient is [tex]x^2-6x+4[/tex], and the remainder is zero (which indicates that x+2 is a factor of p(x)).
--
Edit: long division
We may also solve this problem using long division (see the second image). The first step is to look at the leading coefficients: since [tex]x \times x^2[/tex] is equal to [tex]x^3[/tex], the first term in the quotient will be [tex]x^2[/tex]. Since [tex]x^2 \times (x+2)[/tex] is equal to [tex]x^3+2x^2[/tex], we must now subtract that from [tex]x^3-4x^2-8x+8[/tex].
We repeat the same process, as shown in the image. Since we eventually get to zero, the remainder is zero, and the polynomial at the top (x^2-6x+4) is the quotient.
I know this might be difficult to follow, so please comment if you have any questions.
Related Questions
Dec 18, 11:45:23 AM
Angle A and Angle Bare complementary angles. If m angle A = (4x – 28)° and m
Angle B= (x - 2)°, then find the measure of angle A.
Submit Answer
Answer:
Answers
Answer: 68*
Step-by-step explanation: In pic
On Monday, Byron spent $8.00 on lunch to purchase two tacos and one burrito. On Wednesday, he purchased one enchilada, one taco, and one burrito and spent $8.50. On Friday, it cost Byron $10.00 for two enchiladas and two tacos. If t represents the cost of a taco, b represents the cost of a burrito, and e represents the cost of an enchilada, which system of equations can be used to find the cost of each?
Answers
Answer:
2t+b=8
e+t+b=8.5
2e+2t=10
How can you multiply positive and negative fractions?
Answers
Step-by-step explanation:
When you multiply a fraction by another fraction or a fraction by a whole number, the rules of fractions dictate the form of the answer. If at least one of the values is negative, you also use the rules for positive and negative signs to determine if the result is positive or negative.
Select the locations on the number line to plot the points 9/2 and −7/2.
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Answer:To plot these points on the number line, you should label the long lines on the number line as such starting from the left (-5-already there, -4,-3,-2,-1,0,1,2,3,4,5-already there).
Now take each number and convert the improper fraction into a mixed number. 9/2 = 4 1/2 and -7/2 = -3 1/2.
4 1/2 would plotted on the line exactly in between the 4 and 5.
-3 1/2 would be plotted on the line exactly halfway between -3 and -4.
You will draw a dot to show each of these positions on a number line.
Step-by-step explanation:
hope it helps
There is a leaky faucet in a bathroom, and Joey places a bucket underneath the faucet. After 2/3 of an hour, 1/8 cup of water has been collected in the bucket. At what rate, in cups per hour, is water leaking from the faucet?
A. 1/12
B. 3/16
C. 13/24
D. 19/24
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please help-
Answers
Answer:c
Step-by-step explanation:
i think
Answer:
B
Step-by-step explanation:
You have to divide the fractions and make the answer a reciprocal.
Hope this helps!
find the slope of the line that would be parallel to the given original line 3x+y=10
Answers
can someone please help me with this it’s due soon please
Answers
Answer: 5 inches
Step-by-step explanation:
Perpendicular bisectors must be split directly in half, as they are *bi*sectors, meaning "*two* sections"
Perpendicular means when two angles come together to create a 90° angle
This means that angle BDA is also a 90 degree angle
Since line AC is the line segment split by the perpendicular line segment BD, then you can assume that it is the only 8 inch line, according to multiple laws of geometry. This indicates that segment BC and segment BA must be congruent.
Find the value of x (Round to the nearest tenth) **Hint: Find the length
of the dotted line first***
Helppp!!!!!!!
Answers
Answer:
Length equal 12
Step-by-step explanation:
16^2+b^2=20^2
256+b^2=400 (subtract 256 on both sides)
b^2=144 (square root)
b=12
Explain what the slope of each line below represents. Then find the slope and give its units
Answers
Answer:
The slope represents the rate of change of water volume stored in a storage tank.
The slope here is -900 in units of gallons per month. (gal/mos)
Step-by-step explanation:
The slope is rise over run, going from left to right.
Looking at the difference in time then, it is a period of ten months, and the volume difference is -9000 gallons.
The slope then is -9000 gallons divided by 10 months, which is -900 gallons per month
Suppose you have a dog-walking business after school for which you charge each customer $3 per hour plus an additional $10. What equation could be written to show this relationship?
Answers
Derek needs 2 gallons water to mix a sport drink , but he only has a 1 cup measuring cup.
Answers
Answer:
He can fill up his fill up his measuring cup 8 times that is pretty simple
Step-by-step example
4 cups is in one gallon
A top swimmer would be able to swim across a 25-meter pool in about 15 of a minute. How fast can a top swimmer go?
Answers
Answer:
1.66 or 1 and 2/3 fast
Step-by-step explanation:
Answer:
ಠ ,,ಠ
____
Step-by-step explanation:
because earth is round the amount of time it takes to eat a tortilla chip is honey bunches of oats.
It took the Hendersons 6 1/4 hours to
travel 325 miles.
At this rate, how many miles could they
travel in one hour?
Answers
Answer:
52 miles
Step-by-step explanation:
They drive 325 miles in 6 1/4 hours. Convert 6 1/4 to 6.25 and divide. 325/6.25= 52 mph
Please help me find tge answer soon thxs
Answers
Answer:
acute
Step-by-step explanation:
It measures less than 90 degrees
Answer:
Acute angle
Step-by-step explanation:
(less than 90°)
A new cell phone costs $625. Its sale price is $500. What's the percent of decrease?
Answers
Answer:
20 percent
Step-by-step explanation:
I need points!!!
500/625 = the percent of original
100 - percent of original = answer
M (3, –6) is rotated 90° counterclockwise. (x, y) → (–y, x) 1. Switch the x- and y-coordinates: (6, –3) 2. Multiply the new x-coordinate by –1: (6(–1), –3) 3. Simplify: (–6, –3) Mary Beth used the mapping rule to find the coordinates of a point that had been rotated 90° counterclockwise around the origin. Examine the steps to determine whether she made an error. The student made .
Answers
Answer:
The answer is below
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.
If a point (x, y) is rotated 90° counterclockwise, its new coordinate is (–y, x).
Give point M (3, –6) is rotated 90° counterclockwise:
Step 1: Interchange the x- and y-coordinates to get (-6, 3)
Step 2: Multiply the new x-coordinate by –1 to get (-6(–1), 3)
Step 3: Simplify to get (6, 3)
Therefore she made an error in step 1
Answer: An error in step one
Step-by-step explanation:
please help!! question in picture
Answers
There are 75 new houses being built in a neighborhood. Last month, 2/5 of them were sold. This month, 3/5 of the remaining houses were sold. How many houses are left to be sold?
Answers
Step-by-step explanation:
75 * (1-2/5) * (1-3/5) = 18.
write the equation of the horizontal line that goes through (-5,7)
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Answer:
The equation would be y=7
PLEASE Help ASAaP will give brainlist
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Graph the line with the equation y=-1/2x+1
Answers
Step-by-step explanation:
it depends how far you want to take the equation
Please help I’ll mark you brainlist
Answers
Answer:
∠ MDF = 39°
Step-by-step explanation:
∠ MDH = 90°, so
∠ MDF + ∠ FDH = 90 , substitute values
2r + 59 + 6r + 111 = 90 , that is
8r + 170 = 90 ( subtract 170 from both sides )
8r = - 80 ( divide both sides by 8 )
r = - 10
Thus
∠ MDF = 2r + 59 = 2(- 10) + 59 = - 20 + 59 = 39°
I’ll mark you brainlist help
Answers
This is the answer
y = -4x - 2
Work: The line crosses the y-axis at -2 making this the y-intercept. To find the slope, you need to take two points from the graph (you already have (0,-2) from the intercept) and put them in the equation:
y(sub 2) - y(sub 1) all over x (sub 2) over x (sub 1). Sub 1 and two just means the order of the points. so if you took the points (-1,2) and (0,-2), the equation would look like:
(-2-2)/(0-(-1)). This gives you -4/1 which is equal to -4. So now you have your y intercept (-2) and your slope (-4) so you put it into slope - intercept form:
y=mx + b where m is slope and b is y-intercept
Answer:
The answer to your question is -4x -2
Step-by-step explanation:
Hope I helped have a wonderful day! Plz dollow me! ;) Happy Holidays!!! Bye!/
I need help with my homework this is hard pls help thx!
z=m-x solve for x
Answers
Answer:
x = m - z
Step-by-step explanation:
z = m - x add x to both sides
z + x = m - x + x
z + x = m subtract z from both sides
z - z + x = m - z
x = m - z
Answer:
-z + m = x
Step-by-step explanation:
z = m-x
subtract the m from both sides
z-m = -x
you can't have a negative x so multiply everything by -1
-1(z-m = -x)
-z + m = x
SOMEONE HELP!!!! Garrett must inspect a bridge that goes over a river. He begins 18 feet above water level to inspect the lighting, descends 32 feet to inspect the base of the bridge underwater, then descends another 4 feet to check on the concrete anchoring the base. Which best represents Garrett’s position with respect to the water level?
–54 feet
–30 feet
–18 feet
–10 feet
Answers
Answer:
-18 feet
Step-by-step explanation:
18-32-4
18-36= -18
Answer:
–18 feet
Step-by-step explanation:
Given: Garrett begins 18 feet above water level to inspect the lighting, descends 32 feet to inspect the base of the bridge underwater, then descends another 4 feet to check on the concrete anchoring the base.
Ken gets injured and has to slow the pace he walks. The equation for his new plan is y = -200x +2400 where y is the number of calories left to burn and x is the hours Ken walks. When will ken have 600 calories left to burn.
Answers
Answer:
x=9
Step-by-step explanation:
600=-200x + 2400
-2400
-200x = -1800
x = 9
How much are these coins worth?
Answers
Answer:
$1.97
Step-by-step explanation:
What algebraic expression will I put for the drawing above?
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Please help on these
Answers
Answer:
x should be 11
Step-by-step explanation:
What we know:
The angles shown are 13x + 12, and 2x + 3
The two angles are complementary, which means they equal 180 degrees.
(13x + 12) + (2x + 3) = 180
15x + 15 = 180
15x = 180 - 15
15x = 165
x = 11
please help!! I NEED IT VERY BADLY
Answers
Answer:
3/4
Step-by-step explanation:
tan A =opposite/adjacent = 6/8 =3/4
Hope this helps
Have a good day