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
saveliy_v [14]
3 years ago
5

What is the quotient: (6x4 + 15x3 + 10x2 + 10x + 4) ÷ (3x2 + 2)?

Mathematics
2 answers:
mario62 [17]3 years ago
7 0
<span>                  2x^2 + 5x + 2
3x^2 + 2    </span><span>6x^4 + 15x^3 + 10x^2 + 10x + 4
             -    6x^4                + 4x^2
                             15x^3 + 6x^2 + 10x + 4
             -               15x^3            + 10x
                                           6x^2 + 4
                                           6x^2 + 4

Therefore, </span><span>(6x^4 + 15x^3 + 10x^2 + 10x + 4) ÷ (3x^2 + 2) = </span><span>2x^2 + 5x + 2</span>

Kryger [21]3 years ago
4 0

Answer:  Option 'C' is correct.

Step-by-step explanation:

Since we have given that

\frac{\left(6x^4+15x^3+10x^2+10x+4\right)}{\left(3x^2+2\right)}

Now, we will find the quotient by factoring the numerator:

\mathrm{Use\:the\:rational\:root\:theorem}\\a_0=4,\:\quad a_n=6\\\\\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:4,\:\quad \\\mathrm{The\:dividers\:of\:}a_n:\quad 1,\:2,\:3,\:6\\\\\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:4}{1,\:2,\:3,\:6}\\\\-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2\\\\=\left(x+2\right)\frac{6x^4+15x^3+10x^2+10x+4}{x+2}\\\\=\frac{6x^4+15x^3+10x^2+10x+4}{x+2}=6x^3+3x^2+4x+2\\\\

Now, we will factor it again:

=\left(6x^3+3x^2\right)+\left(4x+2\right)\\\\=2\left(2x+1\right)+3x^2\left(2x+1\right)\\\\=\left(2x+1\right)\left(3x^2+2\right)

At last we get our factorised form :

=\left(x+2\right)\left(2x+1\right)\left(3x^2+2\right)\\\\=\frac{\left(x+2\right)\left(2x+1\right)\left(3x^2+2\right)}{3x^2+2}\\\\=\left(x+2\right)\left(2x+1\right)\\\\=2x^2+5x+2

Hence, Option 'C' is correct.

You might be interested in
If the data analyst hypothesizes that grocery sales are lower on Sunday than on other days, the null hypothesis would likely sta
nlexa [21]

Answer:

The answer is "Grocery sales are lower or no different on Sunday than on other days"

Step-by-step explanation:

Its null hypothesis does not always consider any discrepancy between both the comparable qualities throughout facts and figures. Furthermore, researchers recommend also have lower or even no opposite transactions for Sunday than with other days, because there is no connection between grocery sales and Saturdays and Sundays.

7 0
3 years ago
Which fraction is equivalent to 16/20 ?A.8/100 <br> B.6/10<br> C.48/60<br> D.20/24
denis23 [38]

Answer:

Step-by-step explanation:

16/20 = 48/60

960 = 960

Answer is C

3 0
2 years ago
Read 2 more answers
#9 - The Question
melamori03 [73]

Answer:

  12

Step-by-step explanation:

There are many ways to approach this problem. I like a method that uses the least amount of computation. We could figure how much Wendy makes on a bag of chips, the additional amount Wendy wants to make, then divide the latter by the former to find the number of additional bags to sell.

We could use a proportion to figure the number of bags corresponding to $126 in earnings, then subtract the 72 bags already sold. Essentially, we will do this, but without the intermediate numbers.

__

The additional fraction of 72 bags will be ...

   (126/108) -1 = 18/108 = 1/6

Then Wendy must sell an additional ...

  (1/6)×(72 bags) = 12 bags

to increase her earnings to $126.

7 0
3 years ago
What two other forms to write 8.517
Lena [83]
8.517 in written form is: 

Eight and five hundred seventeen thousandth

8.517 in expanded form is:

8 + 0.5 + 0.01 + 0.007

<span>Hope I Helped You!!! :-)

Have A Good Day!!!</span>
3 0
3 years ago
Read 2 more answers
1. If OQ and RT are parallel lines which statement is true?
Kaylis [27]

Answer:

Step-by-step explanation:

Question (1).

OQ and RT are the parallel lines and UN is a transversal intersecting these lines at two different points P and S.

A). ∠OPS ≅ ∠RSU [corresponding angles]

B). m∠OPS + m∠RSP = 180° [Consecutive interior angles]

C). m∠OPS + m∠OPN = 180° [Linear pair of angles]

D). Since, ∠OPS ≅ ∠TSP [Alternate interior angles]

    And m∠TSP + m∠TSU = 180° [Linear pair of angles]

Therefore, Option (A) is the correct option.

Question (2).

A). m∠RSP + m∠RSU = 180° [Linear pair of angles]

B). m∠RSP + m∠PST = 180° [Linear pair of angles]

C). ∠RSP ≅ ∠TSU [Vertically opposite angles]

D). m∠RSP + m∠OPS = 180° [Consecutive interior angles]

Therefore, Option (C) will be the answer.

3 0
2 years ago
Read 2 more answers
Other questions:
  • P(A)=0.22 and P(B)=0.46 <br> Find P(A OR B)
    13·1 answer
  • Does anyone know the answer to this?
    6·2 answers
  • X=5y<br> 3x=7y+16 <br><br> substitution method, algebra 1
    5·1 answer
  • Help 40 points !!
    7·1 answer
  • A bike store sells scooters at a 54% markup. If the store bought each scooter for $29.25, what is the resale price to the neares
    8·1 answer
  • lisa drank 1/3 quart of orange juice and lane drank 1/2 quart of orange juice. how many quarts did they drink together
    7·1 answer
  • Need some help with multiplying algebraic fractions
    7·1 answer
  • Can someone tell me the graph pls i’ll give you brainlist and points plz
    7·1 answer
  • A Rectangular‘s perimeter and it’s area have the same numerical value. The width of the rectangle is 3 units. What is the length
    9·1 answer
  • Jake noted that speed of light is approximately 1.1 x 10^9 km/h;
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!