There's probably a more efficient way to do it, but the following method works.
First, note that
x² - x - 2 = (x + 1) (x - 2)
Now use synthetic division to divide
a x⁴ + b x³ - x² + 2x + 3
by the two factors above.
Division by x + 1 :
-1 | a b -1 2 3
… | -a a - b -a + b + 1 a - b - 3
= = = = = = = = = = = = = = = = = = = = = = = = = = = = =
… | a b - a a - b - 1 -a + b + 3 a - b
which is to say,
(a x⁴ + b x³ - x² + 2x + 3) / (x + 1)
= a x³ + (b - a) x² + (a - b - 1) x + (-a + b + 3) + (a - b) / (x + 1)
Division by x - 2 :
2 | a b - a a - b - 1 -a + b + 3
… | 2a 2a + 2b 6a + 2b - 2
= = = = = = = = = = = = = = = = = = = = = = = = = = =
… | a a + b 3a + b - 1 5a + 3b + 1
meaning,
(a x³ + (b - a) x² + (a - b - 1) x + (-a + b + 3)) / (x - 2)
= a x² + (a + b) x + (3a + b - 1) + (5a + 3b + 1) / (x - 2)
Putting everything together, we have
(a x⁴ + b x³ - x² + 2x + 3) / (x² - x - 2)
= a x² + (a + b) x + (3a + b - 1) + (5a + 3b + 1) / (x - 2) + (a - b) / (x² - x - 2)
Combine the remainder terms:
(5a + 3b + 1) / (x - 2) + (a - b) / (x² - x - 2)
= ((5a + 3b + 1) x + (6a + 2b + 1)) / (x² - x - 2)
We're given that the remainder is 3x + 5, so
5a + 3b + 1 = 3
6a + 2b + 1 = 5
Solve this system for a and b :
5a + 3b = 2
6a + 2b = 4
5a + 3b = 2
3a + b = 2
5a + 3b = 2
-9a - 3b = -6
(5a + 3b) + (-9a - 3b) = 2 + (-6)
-4a = -4
a = 1
5 • 1 + 3b = 2
3b = -3
b = -1
How to do this please help
Answer:
Step-by-step explanation:
They're asking for the initial fuel, which is how much it had when the distance was 0. so 500, your y-intercept
Answer:
500 litres
Step-by-step explanation:
the relation between the time spent walking and driving if you walk at 3 miles per hour then hitch a ride in a car traveling at 75 miles per hour covering a total distance of 60 miles
Answer:
56 miles
Step-by-step explanation:
Find the simple interest: Principal: $3020 Interest Rate: 5% Time: 6 months
Answer:
A = $3094.58
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Simple Interest Rate Formula: A = P(1 + r)ⁿ
A is the final amountP is the principal amountr is the raten is the time (in years)Step-by-step explanation:
Step 1: Define variables
A = ?
P = 3020
r = 0.05
t = 6 months = 0.5 years
Step 2: Solve for A
Substitute: A = 3020(1 + 0.05)^0.5Add: A = 3020(1.05)^0.5Evaluate: A = 3020(1.0247)Multiply: A = 3094.58And we have our final answer!
Which point is on the graph of x = 1/3(y-18) in the coordinate plane
Answer:
0,-6
Step-by-step explanation:
Help with math! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help! Please! Help!
Answer:
Yes, because two decimals below 1 multiplied together will always make a smaller number than either of the beginning numbers.
Answer:
yes
Step-by-step explanation:
Do lure colors influence Pacific halibut's desire to take the bait? To find out researchers selected 750 Pacific halibut
from a fish farm in California. Half of the fish were randomly assigned to a sparkly, brightly colored fishing lure, while
the other half were assigned to one with a neutral tone and no sparkle. On average, the halibut were more attracted
to the sparkly, bright colors. Which of the following is the largest population to which the results of this survey should
be generalized?
Answer: B
Step-by-step explanation:
i got chegg
How many terms are in 2x-7+y?
.......
3
Step-by-step explanation:
There is three terms
Brainliest if you provide a valid answer.
*Guys, I shouldn't have to say this. Please quit stealing my points. I work pretty hard for them to help people out and I need help answering my questions. I don't think you'd appreciate it if I stole your points.*
Q: Three runners are training for a marathon. One day, they all run about ten miles, each at their own constant speed. Which of the three runners has the fastest pace? Remember to provide an explanation! :)
Answer:
runner #1
Step-by-step explanation:
the ratio of distance to time is as shown:
runner 1: 10:1
runner 2: 8.5:1
runner 3: 9:1
because runner #1 has the highest distance to run ratio, that runner has the fastest pace.
Hope this helps :)
solve for x. please help
Answer:
22
Step-by-step explanation:
Given that polygons ABCD is similar to KGHJ Set up a proportion and solve for X
Answer:
9
Step-by-step explanation:
3/16=x/48
cross multiply
16x=48*3
16x=144
x=9
What is 17.4% of 8350
Answer:
1452.9 or 14529/10Step-by-step explanation:
17.4% of 8350 equals 1452.9 or 14529/10
Hope this helps! <3
if cade shoots 359 free throw shoot in 4 hour, how many can he shoot in 6 hours
Answer:
He will shoot 540
Step-by-step explanation:
I got this answer by dividing 359 by 4 to get how many he gets in 1 hour which is 90 then I multiplied it by 6 and I got 540
Hope I helped
How do I solve this properly?
Answer:
x [tex]\geq[/tex] 4
Step-by-step explanation:
4x^2 - 64 [tex]\geq[/tex] 0 ; move 64 over
4x^2 [tex]\geq[/tex] 64 ; divide by 4
x^2 [tex]\geq[/tex] 16 ; take square root of both sides
x [tex]\geq[/tex] 4
HALP Can someone explain why this is a math question
question:How does the mass of a robot affect the amount of force needed to move or pick up another object?
Answer:
If the robot has more mass, then it will take a bigger force to lift up another object. If the robot is going to lift something up, it will use its arms, and its arms have mass, and the object has a mass as well. If the robot's arms have a mass of 10kg, and the object has a mass of 12kg, it will use a certain amount of force to lift up the object using it's arms. If the the robots arms were 5kg instead, it would take less force to lift of the same object using its arms.
how many roots. real or complex doses the polynomial 7+5x^4-3x^2
Answer:
4 roots
Step-by-step explanation:
Assuming the exuation is
7+(5x^4)- (3x^2)
the polinomial has 4 roots
because a polynomial always has as many roots as it's highest degree
Answer:
4 complex roots
Step-by-step explanation:
My question has been answered
1 half gallon of ice cream cost 4.36 what is the unit price per quart
Answer:
$2.18
Step-by-step explanation:
since there are 4 quarts in a gallon then there are 2 in a half gallon and therefore if you divide by 2 that would be your price per quart.
you have $20 to spend on a taxi fare. The ride costs $5 plus $2.50 per kilometer.
Answer:
What is the question?
Step-by-step explanation:
Answer:
Im gonna assume you want to know how far you can get with the entire 20$
Step-by-step explanation:
so its 5$ already and 2kilometers is another 5. SO you can get 6 kilometers with all of your 20$
10.2 4/5 times 1 2/3
Answer:
14/3
Step-by-step explanation:
A: 10
B: 70
C: 30
D: 90
Tommy picked 15 crayons from a box. if 3 out of the 5 crayons were yellow how many crayons are yellow?
9
13
6
3
What is the domain and range for the function f(x)=0.3x +100
Answer:
Domain: -INFINITY , INFINITY
Range: -INFINITY , INFINITY
Step-by-step explanation:
What is the value of the inequality?
Answer:
The answer is(A) -23
Step-by-step explanation:
that's it
The value of an explanatory variable is 23, while the corresponding value of the response variable is 9. What would be the coordinates of this data point when plotted on a scatterplot? A. (9, 32) B. (23, 9) C. (32, 9) D. (9, 23)
Answer:
(23,9)
Step-by-step explanation:
The Coordinates of this data point when plotted on a scatterplot is (23, 9).
The Correct option is (B)
What are Coordinates?Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).
Given:
The value of an explanatory variable is 23.
and, the value of the response variable is 9.
Now, the explanatory variable represents the x- coordinate and the response variable represents the y- coordinate.
Then, the coordinates of this data point is in form of (x, y) i.e., (23, 9).
Learn more about Coordinates here:
https://brainly.com/question/28806463
#SPJ2
67x(45)/16=x??
lllllllmmmmmmmmmmm sssssssssssssssssssssssssssooooooooooooooo borde
Answer:
Step-by-step explanation:
hahahaha
IIIIIIIIIImmmmmmmmmssssssssssssssssssssssooooooooooooooo borde
Someone help with this I wanna double check my answer
Answer:
C 90
Step-by-step explanation:
Because 5 x 3 is 15 and 2 x 3 is 6 so 15 x 6 = 90!!!!!!
What is the factored form of 36x4 – 25?
(6x2 – 5)(6x2 + 5)
(6x2 – 5)(6x2 – 5)
(6x2 – 25)(6x2 + 25)
(6x2 – 25)(6x2 – 25)
Answer:
Your answer would be A - (6x^2 – 5)(6x^2 + 5)
Step-by-step explanation:
Got it right on Edge 2020-21. Hope this helps, have a great day! :)
2900 loan for 5 months at 8.95% simple interest
Answer:
108.1458
Step-by-step explanation:
Simple interest=(2900×5×8.95)/100×12
=2900×5×895/120000
=29×5×895/1200
=129775/1200
=108.1458
So the simple interest is 108.1458
There are 100 coffee drinkers, 50 take sugar, 60 take cream, and 30 take both cream and sugar. How many take no cream or sugar? (permutation)
Answer:
20 take no cream or sugar.
This afternoon Shelley left school, rode the bus 3/5 of a mile, and then walked 1/5 of a mile to get
home. How much farther did Shelley ride than walk?
Write your answer as a fraction or as a whole or mixed number.
Help Please ASAP! :)
Answer:
2/5 of a mile!
Step-by-step explanation:
Answer:
2/5
Step-by-step explanation:
Her home is 4/5 a mile away from school.
She took the bus 3/5 miles to her house, then walked 1/5 a mile to her house.
3/5-1/5 = 2/5
btw what r u studying on, just curious cause it looks like u studying in a bathtub