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

When 0.5(20x – 50y + 36) – 0.25(–100x + 40y – 12) is simplified, what is the resulting expression?
10x-25y+18-25x+10y-3
-15x-15y+15
-10x+25y+18+25x-10y+3
35x-35y+21

Answers

Answer:

35x-35y+21

Step-by-step explanation:

You would have to combine the like terms together to get 35x-35y+21.

By applying algebra properties we notice that the algebraic expression 0.5 · (20 · x - 50 · y + 36) - 0.25 · (- 100 · x + 40 · y - 12) is equivalent to 35 · x - 35 · y + 21. (Correct choice: D) #SPJ5

How to simplify an algebraic expression

In this question we must simplify an algebraic expression by applying the following list of properties:

Commutative propertyAssociative propertyModulative propertyDistributive propertyExistence of additive inverseExistence of multiplicative inverse

Now we proceed to simplify the expression given in the statement:

0.5 · (20 · x - 50 · y + 36) - 0.25 · (- 100 · x + 40 · y - 12)     Given

10 · x - 25 · y + 18 + 25 · x - 10 · y + 3     Distributive and associative properties/Definition of multiplication

35 · x - 35 · y + 21     Result

By applying algebra properties we notice that the algebraic expression 0.5 · (20 · x - 50 · y + 36) - 0.25 · (- 100 · x + 40 · y - 12) is equivalent to 35 · x - 35 · y + 21. (Correct choice: D) #SPJ5

To learn more on polynomials, we kindly invite to check this verified question: https://brainly.com/question/11536910 #SPJ5

Find the 92nd term of the arithmetic sequence -29, -22, -15, ...

Answers

Answer:

608

Step-by-step explanation:

The appropriate general formula here is a(n) = a(1) + (n -1)d, where d is the common difference.  Here, d = +7.  Thus:

a(92) = -29 + (92-1)(7) = 608

Please help I have 30 mins

Answers

Answer:  0.6 in 10 % ; 0.4 in 15 %

Step-by-step explanation:

1. (x*10%) + (y*15%)/ x+y=12%

2. x+y = 1  x= 1-y

(0.1x + 0.15y/ x+y= 12/100) * 100

(10x + 15y/x+y = 12)*(x+y)

10x+15y= 12x + 12y

-2x=-3y

2x = 3y   2(1 - y)= 3y

2-2y=3y   2= 5y

y= 0.4

x= 0.6

The diameter of a circle is 5 cm. Find its area to the nearest tenth.

Answers

78.5 bc 5^2 is 25 so 25x Pi or 3.14 is 78.5

help me pleaseeeeeeeeeeeeeeeee

Answers

Step-by-step explanation:

-d=0.8-1.5

-d=-0.7

d=0.7

Answer:

d=0.7

Step-by-step explanation:

1.5=d+0.8

d=1.5-0.8

d=0.7

What is the solution of the system of equations shown in the graph below?

Answers

Answer:

The point on the plane (4, 2)

That is x = 4 and y = 2

Step-by-step explanation:

Look for the point where the two lines given by the system of linear equations  intersect. That point is (4, 2)

x = 4 and y = 2

Suppose $5,000 is divided into two bank accounts. One account pays 5% simple interest per year and the other pays 7% per year. If after one year there is a total of $310 in interest between the two accounts, $3,000 was invested at 5%

Answers

Answer:

What is the question?

Step-by-step explanation:

Which would be an estimate for 36,004 ÷ 853

Answers

Answer:

42.21

Step-by-step explanation:

Answer:

42.2086752638

Step-by-step explanation:

calculator

bag contains 150 jelly beans. Toros reached into the bag 20 times and randomly selected one jelly bean. Each time, he recorded the color of the jelly bean, placed it back in the bag, and then mixed the jelly beans.

The following table represents the number of times Toros chose each color of jelly bean.
Based on these results, what is the probability that the next jelly bean Toros draws out of the bag will be yellow?

Answers

Ok so 150 total right? Divide that by 20 than multiply the picked up beans to find the probability of pulling a yellow jelly bean. That’s is 150/20=7.5 or 15/2. 3 (yellow jelly beans) is multiples by 7.5 which gives 15/100 chances of getting a yellow jelly bean in your next pull. Now simplify that, your welcome.

5. help me i’ll give you brainliest if u get this right

Answers

Answer: D.) 2

Step-by-step explanation:

In a rhombus, all sides are congruent; they have the same lengths (like a square). This means that if this parallelogram was a rhombus, 14 - x and 2x + 8 will have to be equal.

14 - x = 2x + 8

Subtract 2x from both sides

14 - 3x = 8

Subtract 14 from both sides

-3x = -6

Divide both sides by -3

x = 2

the table shows running speeds of 10 randomly selected lions.

speed (miles per hour) 48, 45, 50, 44, 46, 45, 42, 47, 45, 48. based on the data

select the most reasonable prediction about the speed of the lion

A. the top speed of a lion is 48 miles per hour.
B. the typical lion runs at a speed of about 46 miles per hour.
C. the typical lion runs at a speed of about 40 miles per hour.
D. the typical lion runs at speeds greater than 50 miles per hour.

Answers

Answer:

I think B

Step-by-step explanation:

Find the average

Answer:

B

how i know: i took the test

The sum of two numbers is 58. The difference between the same two numbers is 6. Find the two
numbers, and then find the PRODUCT of the two numbers.
The product of the two numbers is 32
The product of the two numbers is 58
The product of the two numbers is 832
The product of the two numbers is 64

Answers

Answer:

The product of the two numbers is 832

Step-by-step explanation:

x+y= 58

x-y=6

2x = 64

x = 32

y = 26

32*26=832

37=-3+5(x+6), Please provide explanation.

Answers

Answer:

x=2

Step-by-step explanation:

youd distribute the 5 first so the equation is now

37=-3+5x+30

then group the common terms (-3 and 30 in this case)

37=5x+27

now subtract 27 from both sides to start to isolate 5x

10=5x

divide by 5 to find x

2=x

hope i helped :)

37=−3+5(x+6)
37 = -3 + (5)(x) + (5)(6)
37 = -3 + 5x + 30
37 = (5x) + (-3 + 30)
37 = 5x + 27
5x + 27 =37
5x + 27-27 = 37-27
5x= 10
Divide 5 on both side and you get x= 2

find the value of d.
1/2d - 5 -1/4d = 10

Answers

d=60. multiply both sides of the equation by 4 since it’s a factor, giving you 2d-20-d=40. since there are like terms with d, collect them to get d-20=40 and move 20 to the right and change it’s sign. that will give you d=40+20, then calculate to get d=60. hope this helped! :)

A school store has 1200 pencils and sells 25 per day the manager reorders when the number of pencils in stock is 650

Answers

Answer:

He reorders after 22 days

Answer:

(1200÷25) ÷ans= days

Step-by-step explanation:

Q:
What is 9.687-3.699?

Answers

Answer:

5.988

Step-by-step explanation:

_9.687

3.699

=5.988

Determine the value of the variable that makes each equation true.

Answers

Answer:

-9

-11

-4

Step-by-step explanation:

Is 18/5 and 7/2 proportional

Answers

Answer:

no its not

Step-by-step explanation:

A long-distance delivery truck averages 8 miles per gallon when the truck is full. The
miles per gallon improves by 20% when the truck is empty. If the truck travels 160 miles
full to deliver its goods, and then travels back 160 miles empty, approximately how many
gallons will the truck use in all?

Answers

8 mpg when full
8*1.2=9.6mpg when empty
160/8+160/9.6=36.67

The gas used by truck is 36.66 mpg.

What is linear equation?

When graphed, a linear equation always produces a straight line because it is an algebraic equation with each term having an exponent of 1. It is referred to as a "linear equation" for this reason.

One-variable linear equations and two-variable linear equations exist.

Given

A long-distance delivery truck averages 8 miles per gallon when the truck is full.

The miles per gallon improve by 20% when the truck is empty.

The distance delivery truck averages 8 miles per gallon when full, and the amount of gasoline used (g) is expressed in terms of the number of miles driven ([tex]m_{f}[/tex]).

When the truck is full, the amount of gasoline is shown as,

[tex]m_{f}[/tex] = d/8

given distance is 160 miles

[tex]m_{f}[/tex] = 160/8  = 20 mpg

Then,

The miles per gallon improve by 20% when the truck is empty.

The number of miles driven when empty is represented as,

[tex]m_{e}[/tex] = d/(8 + 1.6)

[tex]m_{e}[/tex]  = d/9.6

[tex]m_{e}[/tex] = 160/9.6

[tex]m_{e}[/tex]  = 16.66 mpg

total gasoline  required = [tex]m_{e}[/tex] +  [tex]m_{f}[/tex]  = 20 + 16.66 = 36.66 mpg

Hence the total  gas used is 36.66 mpg.

Learn more about linear equation;

https://brainly.com/question/29739212

#SPJ2

simplify 2 to the power of 4 times 2 to the power of 6

Answers

Answer:

1/4

Step-by-step explanation:

=2^4×2^-6

=2^-2

=1/4

Answer:

you add the exponents so youd do 4+6 which is 10. and then 2 to the power of 10 is 1024

100 points and a Brainliest

just answer this question



what is dabi real name off of my hero academia

Answers

Answer: Toya Todoroki

Step-by-step explanation:

Answer:

Touya Todoroki

Step-by-step explanation:

i used to watch the show

Lance is drawing a triangle. He draws one side that is 8 inches long and another side that is 5 inches
long. Which one of the following could be the third side?

Answers

Answer:

6 inches

Step-by-step explanation:

(8-5)>x>(5+8)

5.3 lesson 14 problem set answer

Answers

i 100% agree with this statement

A soccer tournament was designed with 512 teams where an eighth of the teams were eliminated after each round. Write a function, f(x), that models the number of teams still in the number of teams still in the tournament after x rounds have been played.

Answers

Answer:

f

Step-by-step explanation:

fsdsdsdwdd

Put the following equation of a line into slope-intercept form, simplifying all fractions. 3y - 40 = 9​

Answers

Answer:

3y=49

Step-by-step explanation:

yeppp I'm pretty sure


The number 160 is increased by 50%. The result is then decreased by 25%. What is the final number?
The final number is what?

Answers

Answer:

60

Step-by-step explanation:

50%=.50

160×.50=80

160+80=240

25%=.25

240×.25=60

60 is the final number


will mark brainlest if correct! pls help

Answers

Answer:

See below.

Step-by-step explanation:

[tex] y_2 = 4x^2 [/tex]

[tex] x = 1 [/tex]

[tex] y_2 = 4(1)^2 = 4 = a [/tex]

a = 4

[tex] y_3 = 4^x [/tex]

[tex] x = 1 [/tex]

[tex] y_3 = 4^1 = 4 = b [/tex]

b = 4

[tex] y_1 = 4x [/tex]

[tex] x = 2 [/tex]

[tex] y_1 = 4(2) = 8 = c [/tex]

c = 8

[tex] y_3 = 4^x [/tex]

[tex] x = 2 [/tex]

[tex] y_3 = 4^2 = 16 = d [/tex]

d = 16

[tex] y_1 = 4x [/tex]

[tex] x = 3 [/tex]

[tex] y_1 = 4(3) = 12 = e [/tex]

e = 12

[tex] y_2 = 4x^2 [/tex]

[tex] x = 3 [/tex]

[tex] y_2 = 4(3)^2 = 36 = f [/tex]

f = 36

[tex] y_3 = 4^x [/tex]

[tex] x = 3 [/tex]

[tex] y_3 = 4^3 = 64 = g [/tex]

g = 64

How do I complete the square for 4x^2+ 8x-5= 0?

Answers

Answer:

man I have no idea dude I don't really know squares if you're talking about square root I really don't know

Answer:

x = [tex]\frac{1}{2}[/tex],  -  [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

This is not so fun!

[tex]4x^{2} + 8x - 5 = 0\\[/tex]

Step 1:  Move the 5 to the right side

[tex]4x^{2} +8x = 5[/tex]

Step 2:  Divide thru by 4

[tex]x^{2} + 2x = \frac{5}{4}[/tex]

Step 3:  Divide 2 (from 2x)  by 2 and square the result and add that to both sides of the equation.

2/2 = 1    1 squared = 1

[tex]x^{2} + 2x + 1 = \frac{5}{4} +1 = \frac{9}{4}[/tex]

Step 4:  Factor the left side

[tex](x + 1)^{2} = \frac{9}{4}[/tex]

Step 5:   Take the square root of both sides

x + 1 = ±[tex]\sqrt{\frac{9}{4} }[/tex] =  ± [tex]\frac{3}{2}[/tex]

Step 6:   Move the 1 to the right side and add the results

x = -1 ± [tex]\frac{3}{2}[/tex] = -1 +  [tex]\frac{3}{2}[/tex]   or -1 -  [tex]\frac{3}{2}[/tex]

              = [tex]\frac{1}{2}[/tex]    or   -  [tex]\frac{5}{2}[/tex]

And bingo, you have the solutions by completing the square.  Lot of fun, huh.  

how many times does the divisor 4 divides into 324

Answers

Answer:

81 times

Step-by-step explanation:

4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4

Taryn buys 8 identical glasses. Her total is $48 before tax. How much did Taryn pay for each pair of glasses?

Answers

Answer:

$12 per pair of glass.

$6 per glass.

Step-by-step explanation:

48/8 = 6

A pair is 2, so I multiplied 6 by 2.

6 x 2 = 12

So, Taryn paired $12 per glass.

--

ANSWER: $12 per pair

EXPLANATION: $48 divided by 8 pairs of glasses equals $6 per glasses. So then you multiply 6 by 2 to get the amount per pair.

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