1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kherson [118]
4 years ago
10

Find the quotient using polynomial long division:

Mathematics
1 answer:
Snowcat [4.5K]4 years ago
8 0

(1) 50y^3=5y\cdot 10y^2, and

10y^2\cdot(5y-4)=50y^3-40y^2

Subtract this from 50y^3+10y^2-35y-7 to get a remainder of

(50y^3+10y^2-35y-7)-(50y^3-40y^2)=50y^2-35y-7

What we've done here is show that

\dfrac{50y^3+10y^2-35y-7}{5y-4}=10y^2+\dfrac{50y^2-35y-7}{5y-4}

We can keep going as long as the degree of the remainder's numerator is at least the same as the degree of its denominator.

Next, 50y^2=5y\cdot 10y, and

10y\cdot(5y-4)=50y^2-40y

Subtract this from the previous remainder to get a new remainder of

(50y^2-35y-7)-(50y^2-40y)=5y-7

which means

\dfrac{50y^3+10y^2-35y-7}{5y-4}=10y^2+10y+\dfrac{5y-7}{5y-4}

Finally, 5y=5y\cdot1, and

1\cdot(5y-4)=5y-4

Subtract this from the previous remainder to get

(5y-7)-(5y-4)=-3

So we end up with

\dfrac{50y^3+10y^2-35y-7}{5y-4}=\boxed{10y^2+10y+1}-\dfrac3{5y-4}

(the quotient is the expression in the box)

(2) Using the same process as before:

8m^4=2m\cdot4m^3

4m^3\cdot(2m+1)=8m^4+4m^3

(8m^4-4m^2+m+4)-(8m^4+4m^3)=-4m^3-4m^2+m+4

\implies\dfrac{8m^4-4m^2+m+4}{2m+1}=4m^3-\dfrac{4m^3+4m^2+m+4}{2m+1}

-4m^3=2m\cdot(-2m^2)

-2m^2\cdot(2m+1)=-4m^3-2m^2

(-4m^3-4m^2+m+4)-(-4m^3-2m^2)=-2m^2+m+4

\implies\dfrac{8m^4-4m^2+m+4}{2m+1}=4m^3-2m^2-\dfrac{2m^2-m-4}{2m+1}

-2m^2=2m\cdot(-m)

-m\cdot(2m+1)=-2m^2-m

(-2m^2+m+4)-(-2m^2-m)=2m+4

\implies\dfrac{8m^4-4m^2+m+4}{2m+1}=4m^3-2m^2-m+\dfrac{2m+4}{2m+1}

2m=2m\cdot1

1\cdot(2m+1)=2m+1

(2m+4)-(2m+1)=3

\implies\dfrac{8m^4-4m^2+m+4}{2m+1}=\boxed{4m^3-2m^2-m+1}+\dfrac3{2m+1}

You might be interested in
A jar contains nickels and dimes. There are 16 coins in the jar and the total value of the coins is $1.00. Which system of equat
Anna11 [10]

Answer:

12 nickels and 4 dimes

Step-by-step explanation:

5 x 12 = 60 cents  

10 x 4 = 40 cents

             _______

             100 = 1 dollar

4 0
3 years ago
What are numbers 6-8? Please help!!!
salantis [7]
6. The answer is 208

8. The answer is 285
7 0
3 years ago
Read 2 more answers
The graph of a linear function is shown on the grid.
Elza [17]

Answer:

Option (A)

Step-by-step explanation:

Let the equation of the line passing through a point (x', y') and slope 'm' is,

y - y' = m(x - x')

Slope of the line passing through two points (0, 5) and (4, -7),

m = \frac{y_2-y_1}{x_2-x_1}

   = \frac{5+7}{0-4}

   = -3

As slope of the line is negative, Options (A) and (B) will be the possible options.

Therefore, equation of the line passing through (4, -7) will be,

y - (-7) = -3(x - 4)

y + 7 = -3(x - 4)

Therefore, Option (A) will be the correct option.

6 0
3 years ago
Read 2 more answers
PASSES THROUGH (-4,0) ,SLOPE=2
oksian1 [2.3K]

Answer:

y=2x+8

Step-by-step explanation:

6 0
3 years ago
100 POINTS FOR ANSWERS AND BRAINIEST WITH THANKS AND RATING
lisabon 2012 [21]

Commutative property of addition:

a + b = b + a

Associative property of addition:

a + (b + c) = (a + b) + c

Opposite of a sum:

- a - b = - (a + b)

If we look at the options, A and D follow associative property.

B follows commutative property.

C follows opposite of a sum property.

3 0
4 years ago
Other questions:
  • Cost to store 56$ markup 80%
    5·1 answer
  • Write a function for the table
    11·2 answers
  • What is the output value for the following function if the input value is 4?
    15·1 answer
  • Giving brainliest What is the value of x? A right angle is shown divided into two parts. The measure of one part of the right an
    11·1 answer
  • What’s eighty thousand, nine hundred twenty-three and eighty-six hundredths
    14·2 answers
  • How long did it take to reach the bottom of the slope
    12·1 answer
  • Which segments are parallel?
    5·1 answer
  • Is the sequence below arithmetic or geometric? Explain
    12·1 answer
  • What is the slope of a vertical line?<br> What is the slope of a horizontal line?
    15·1 answer
  • Can u show the step and thanks
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!