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
What are the three steps you should use when using algebra to solve word problems?
KonstantinChe [14]
Answer: understand , strategize and implement

Hoped it helped , if it didn’t I apologize
Good luck
3 0
3 years ago
A regular pyramid has a square base with sides of length 1. The four triangular faces are isosceles triangles whose equal sides
lawyer [7]

Answer:

jiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

Step-by-step explanation:

iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

5 0
4 years ago
Help me someone!!!!!!!!!!!!!!!!!!!!!!!
Julli [10]
Substitute answers in, a = 3 and b = 2.

(3^2 - 2^2)/(3+2)
= (9-4)/5
= 5/5
= 1
7 0
3 years ago
a baker used 660 boxes of cake mix to make a wedding cake. if each box called for 3 eggs, how many dozen eggs were used to make
yanalaym [24]
We know there’s 660 boxes and each box called for 3 eggs, therefore:

660=3X

when divide both sides by 3 to isolate the x, which will tell us the amount of eggs used…

660/3 = 220
6 0
3 years ago
Write the equation of a line that is
prisoha [69]

Answer:

y=3/2

Step-by-step explanation:

This line's slope is perpendicular to -2/3 and its y intercept is 0.

4 0
3 years ago
Other questions:
  • Mr. and Mrs. Hartford want to buy a car that cost $8,675 Mr. Hartford saved $1,305 each month for three months Mrs. Hartford sav
    6·2 answers
  • The complex solution to a quadratic equation is below. Write this solution in standard form, a+bi, where a and b are real number
    11·1 answer
  • The original price of a computer was reduced by $250.
    7·2 answers
  • A company is producing two types of ski goggles. Thirty percent of the production is of type A, and the rest is of type B. Five
    10·1 answer
  • What is 30% of 32.95
    11·1 answer
  • Compare how you would model and record finding the sum and difference of two rocks weighing 2/8 & 3/8 of a pound
    5·1 answer
  • 40. When you translate, (x, y+6) will move
    10·2 answers
  • Please help me, i can’t afford to get anything wrong i’m failing /:
    14·1 answer
  • A 2 kg hammer is used to nail a 0.002 kg nail with a force of 10 N. How much force is applied to the hammer?
    5·1 answer
  • A beetle was running along a number line, Then the bug ran from 28 to 78. What distance did it cover? If this run took the bug 9
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!