a
The expression ax²+bx+c is divisible by x-1, has a
remainder of 2 when divided by x+1 and has a remainder of 8 and when divided by x-2 find the values of a, b, and c and
factorise completely.​

Answers

Answer 1

Answer:

(x - 1)(3x + 2)

Step-by-step explanation:

By the Remainder theorem

Given expression is divisible by x - 1 then f(1) = 0

when divided by (x + 1) then f(- 1) = 2

when divided by x - 2 then f(2) = 8

Substitute x = 1, x = - 1, x = 2 into the expression , that is

a + b + c = 0 → (1)

a - b + c = 2 → (2)

4a + 2b + c = 8 → (3)

Subtract (1) from (2) to eliminate a and c

- 2b = 2 ( divide both sides by - 2 )

b = - 1

Subtract (1) from (3) to eliminate c

3a + b = 8 ← substitute b = - 1

3a - 1 = 8 ( add 1 to both sides )

3a = 9 ( divide both sides by 3 )

a = 3

Substitute a = 3, b = - 1 into (1) and evaluate for c

3 - 1 + c = 0

2 + c = 0 ( subtract 2 from both sides )

c = - 2

Then a = 3, b = - 1, c = - 2

Thus

ax² + bx + c

= 3x² - x - 2

= (x - 1)(3x + 2) ← in factored form


Related Questions

please could u help me with this?​

Answers

43.68. You multiply the base by the height

work out the volume of this hemisphere with diameter 9.6 cm

Answers

Answer:

Please refer to the attachment

how to write "The product of a number and -2 increased by 10"? ​

Answers

(x•-2)+10 I’m pretty sure
Possible ways

2(x) + 10

x • 2 + 10

x(2) + 10

Please help I’ll give you the Brainlylist

Answers

Answer:

86

Step-by-step explanation:

Answer:

28/15

--

I hope it helps!

Paragraph One

He drives a racecar 80 miles per hour. He motivates audiences of hundreds. He's earned awards for his performance on and off the racetrack, and he's traveled the country to compete. Did we mention that he's 13 years old? One look at his accomplishments and it is easy to see that Noah "Little Gator" Cornman is on the fast track to success. "Little" might be a part of his nickname, but it does not describe his determination to succeed and his heart to make a difference for kids like him.

In paragraph 1, which sentence implies that the author is impressed with the teen's accomplishments?

He drives a racecar 80 miles per hour.
He motivates audiences of hundreds.
Did we mention that he's 13 years old?
He's traveled the country to compete.

Answers

Answer:

Did we mention that he's 13 years old?

Step-by-step explanation:

because he inspire alot of people by driving a racecar 80 mph that is fast for a kid at his age.

Answer:

Did we mention that he's 13 years old?

Step-by-step explanation:

Did this in middle school 1 year ago it right

Alex was thinking of a number. Alex doubles it the adds 20 to get answer of 22.7. What was his original number.

Answers

Answer:

2.7

Step-by-step explanation:

Let the number alex think be x

Answer = 22.7

According to the question,

x + 20 = 22.7

x = 22.7 - 20

x = 2.7

Therefore, his original number is 2.7

Plz mark me as brainliest

Have a great day

You are at a restaurant. You are ordering a drink. You can choose small or large. Then you can choose between sprite, diet coke, coke, and dr pepper. How many choices or combinations do you have in total? How did you get that answer? What if now you had to choose lid or no lid? And straw or no straw? How many in total?

Answers

Answer:

so in all it's 4.

Step-by-step explanation:

1: for the drink size.

1: for the kind of drink you want.

1: for the lid or no lid.

1: for the straw or no straw

what is the slope of this line, simplify if possible!

Answers

Answer:

The slope is 0

Step-by-step explanation:

the line is straight, so the slope is 0. I hope this helps

f(x) = 5 – 0.2c and g(x) = 0.2(x + 5).

Answers

Answer:

i recommend math-way's they give you step by step or if you are work on Big ideas work use Slader they have all the answers  

Step-by-step explanation:

(q – 5) 7 simplified

Answers

Answer:

7q-35

Step-by-step explanation:

Two groups of students were asked how far they lived from their school. The table shows the distances in miles:


Group A (distance in miles) 1 1.5 3.03 3.2 2.8 1.5 1.8 2.5 2.2
Group B (distance in miles) 2 2.5 3.23 1.3 1.8 2.4 3 1.5 1.8


Which statement best compares the mean distances for the two groups?
It is equal for Group A and Group B.
It is greater for Group B than Group A.
Its value for Group A is double the value for Group B.
Its value for Group B is double the value for Group A.

Answers

Answer:

B

Step-by-step explanation

add all numbers then divide by the number of numbers and you get the means

Answer:

B

Step-by-step explanation:

How many toothpicks make a triangle? Two triangles? Write
an expression that represents the number of toothpicks
needed to make x triangles that appear side-by-side in a
single row, as shown. Explain your reasoning,

Answers

Answer:

3 toothpicks make a triangle  x =3

Step-by-step explanation:

Help me? I’m giving brain

Answers

Answer:

4.31 as said

Step-by-step explanation:

Answer:

it could be 4.30 because when u divide those two the answer is 4.3057142857, and because the number in the hundreths place is just a 0 its probably just 4.30 i could be wrong sorry

subtract -10 from 100​

Answers

Answer:

110

Step-by-step explanation:

Just trust me mate im in 7th grade

Andy wants to rent a limo to go to prom, but wants to split the cost with some friends. The limo costs $400 to rent

Answers

Answer:

its would prob be 100 / 4

Step-by-step explanation:

Can someone pls help me on this

Answers

CF is 7

Step-by-step explanation:

GE is 10 and they have to be equal so 10-3 is 7

Can someone pls help me

Answers

Answer:

10

Step-by-step explanation:

Answer: its an acute angle so its 90

Step-by-step explanation:

Johanne packed 10 boxes of apples each day for 8 days. What is the total number of boxes Johanne packed?

Answers

Answer:

80 10x8 is 80

your welcomr

Solve the following equation:
1/3(y - 2) -5/6 (y + 1) =3/ 4(0 - 3) - 2

Answers

Answer:

11/5

Step-by-step explanation:

If you need help with more problems like this you can use m a t h w a y. (remove the spaces)  :)

Which mathematical term can be defined precisely?
point
line
distance
circle
ASAP

Answers

Answer:

I think it is option A

point

hope it helps

Answer:

point

Step-by-step explanation:

6(1 - 6x) < 38 - 4x
What is the answer to this equation.

Answers

Answer:

x>-1

Step-by-step explanation:

Answer:

x > -1

Step-by-step explanation:

Find the value of x. Round to the nearest degree as needed.

Answers

9514 1404 393

Answer:

  x° = 59°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the trig relations. The one applicable here is ...

  Tan = Opposite/Adjacent

  tan(x°) = 5/3

  x° = arctan(5/3) ≈ 59.04°

The value of x is about 59.

Q2. 1 a) Dave wants to invest $2000 in an account that earns 2.5% interest compounded monthly. If he
leaves the money in the account for 5 years, how much money will he have at the end of those 5 years?

Answers

Question: Dave wants to invest $2000 in an account that earns 2.5% interest compounded monthly. If he  leaves the money in the account for 5 years, how much money will he have at the end of those 5 years?

Answer:

Step-by-step explanation:

help me please :( I'm in 7th grade but I'm only adding this text bc it won't let me ask the question without it lol​

Answers

Answer:

C

Step-by-step explanation:

Decimal Place Question!! Please help :(
3.9931 rounded to 1 decimal place
Only answer if your positive your answer is correct :)

Answers

Answer:

4.0

Step-by-step explanation:

Given that

3.9931

Now rounded to one decimal places

3.9931 = 4.0

So the above value would be rounded to one decimal places after rounded off it comes 4.0

A side of the triangle below has been extended to form an exterior angle of 116. Find the value of x

Answers

Answer:

[tex]x=64 \textdegree[/tex]

Step-by-step explanation:

From the question we are told that

Angle of extension [tex]y=116 \textdegree[/tex]

Generally the angle formed at x is mathematically given as

[tex]x=180-116[/tex]

[tex]x=64 \textdegree[/tex]

Answer:

26°

Step-by-step explanation:

A side of the triangle below has been extended to form an exterior angle of 116°. Find the value of xx.

The answer is 26° i tried 64 and it was incorrect.

1. x-y=1
x+y=-5
2. x-4y=10
2x+y=2
3. -5x+y=0
x+y=6
4. y=6-2x
y=4
5. 2y=16
4x-y= 4
6. x=y -4
3x+y=12
7. y- 2x=-6
5x-y= 9
8. 3y+x= 2
y-x=-6

Answers

Answer:

what is the question write it in thecomments and ill answer

Answer:

1.) (y+1)+y=-5

2y=-6

y=-3

x+(-3)=-5

x=-2

plug in to check if it works

2.) 2(4y+10)+y=2

9y+20=2

9y=-18

y=-2

x-4(-2)=10

x+8=10

x=2

3.) -5(-y+6)+y=0

5y-30=0

5y=30

y=6

x+(6)=6

x=0

4.) 4=6-2x

-2=2x

x=-1

y=6-2(-1)

y=8

5.) 4x-(8)=4

4x=12

x=3

4(3)-y=4

12-y=4

-y=-8

y=8

6.) 3(y-4)+y=12

4y-12=12

4y=24

y=6

x=6-4

x=2

7.) 5x-2x-6=9

3x=15

x=5

5(5)-y=9

25-y=9

-y=-16

y=16

8.)3(x-6)+x=2

4x-18=2

4x=20

x=5

y-5=-6

y=-1

hope this helped :)) also make sure to plug the x and y back into both equations :))

What is the initial value of e=3h+200.

Answers

Answer:h=e-200/3

Step-by-step explanation:

You have 5 3/4 cups of sunflower seeds and 1 1/4 cups of peanuts for birdseed. You use 2/3 of the total mixture each week. How many weeks your birdseed mixture last

Answers

Answer:

Step-by-step explanation:

The bird food lasts 1½ weeks.

Your birdseed mixture last till 10 and a half weeks.

What is an improper fraction?

A fraction that has the numerator higher than or equal to the denominator is said to be an improper fraction.

Given:

You have 5[tex]\frac{3}{4}[/tex] cups of sunflower seeds and 1[tex]\frac{1}{4}[/tex] cups of peanuts for birdseed.

The total mixture,

= 5[tex]\frac{3}{4}[/tex] + 1[tex]\frac{1}{4}[/tex]

= 23/4 + 5/4

= 28/4

= 7 cups.

You use 2/3 of the total mixture each week.

That means,

the number of weeks,

= 7 x 3/2

= 21/2

= 10.5 weeks.

Therefore, the mixture will last till 10 and a half weeks.

To learn more about the improper fraction;

brainly.com/question/21449807

#SPJ2

Angles a and b are complementary angles symmetry of angle a is 28° more than the measure of angle b find the missing angle measures

Answers

Answer:

31 , 59

Step-by-step explanation:

a = b +28

a + b = 90 {Complementary}

b + 28 + b = 90    {Combine like terms}

2b + 28 = 90       {Subtract 28 form both sides}

       2b  = 90 - 28

       2b = 62      {Divide both sides by 2}

        b = 62/2

       b = 31

a = 31 + 28

a = 59

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