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pashok25 [27]
3 years ago
11

Which polynomial is factored completely?

Mathematics
2 answers:
n200080 [17]3 years ago
6 0
G^5 -g = g(g^4 -1)=g(g^2 -1)(g^2 +1) = g(g-1)(g+1)(g^2 +1)

24g^2 -6g^4 = 6g^2(4 -g^2) = 6g^2(2 -g)(2 +g)
d1i1m1o1n [39]3 years ago
5 0

Answer:

The polynomial which is factored completely is  2g^2+5g+4 as these are not further factored.        

Step-by-step explanation:

To find : Which polynomial is factored completely?

Solution :

We factor the given polynomial one by one,

1) g^5-g

g^5-g=g(g^4-1)

g^5-g=g(g^2-1)(g^2+1)

g^5-g=g(g-1)(g+1)(g^2+1)

2) 4g^3 + 18g^2+20g

4g^3 + 18g^2+20g=2g(2g^{2}+9g+10)

4g^3 + 18g^2+20g=2g(2g^{2}+5g+4g+10)

4g^3 + 18g^2+20g=2g[g(2g+5)+2(2g+5)]

4g^3 + 18g^2+20g=2g(2g+5)(g+2)

3) 24g^2 - 6g^4

24g^2 - 6g^4=6g^{2}(4-g^{2})

24g^2 - 6g^4=6g^{2}(2-g)(2+g)

4) 2g^2+5g+4

This expression is can not be factored with rational number as

D=b^2-4ac\\D=5^2-4(2)(4)\\D=25-32\\D=-7

Discriminant D<0 so there is no rational roots.

So, The polynomial which is factored completely is  2g^2+5g+4 as these are not further factored.

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This formula, however, only works if the points don't share any of the two coordinates. Otherwise, one of the two conditions is true:

x_1=x_2,\quad y_1=y_2

And at least one of the denominators in the formula above will vanish.

So, if two points share the same x coordinate, they lie on the vertical line x=k, where k is the shared x coordinate.

Similarly, if two points share the same y coordinate, they lie on the horizontal line y=k, where k is the shared y coordinate.

In your case, the x coordinate is the same, so the points lie on the vertical line x=10.

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Which equation should be used to find the volume of the figure?
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Answer:

Given that

                                                                 1

John can run 100 meters dash in 16    --------- seconds .

                                                                  5

Savanna 's time is 19.8 seconds .

Here we have John time in mixed fraction and Savanna's time in decimal .

Converting mixed fraction into improper .

     1                      16 * 5     +  1                 80 + 1                 81

16  --------    =     ---------------------------    =   -------------- =   - -----------

    5                           5                                  5                      5

Thus we got John time as 81 /5 seconds .

Converting Savanna's time in fraction , we get

 19 8

----------  seconds .

  10  

We have two fractions with different denominator .

One is having denominator 5 and another is having denominator 10 .

We need to make the denominator same of both the fraction .

We need to make denominator 10 .

Multiply John fraction by 2 in both numerator and denominator by 2 to make denominator 10 .

81 * 2               162

----------  =      ------------ seconds .

5 *  2                   10

John is taking less time than Savanna . Thus John is faster .

Difference

198          162            36

-------  -     -------     =  ------- seconds  

10              10              10

Thus John is faster by  (36/10 ) seconds  =  3.6 seconds.

Step-by-step explanation:

Given that

                                                                 1

John can run 100 meters dash in 16    --------- seconds .

                                                                  5

Savanna 's time is 19.8 seconds .

Here we have John time in mixed fraction and Savanna's time in decimal .

Converting mixed fraction into improper .

     1                      16 * 5     +  1                 80 + 1                 81

16  --------    =     ---------------------------    =   -------------- =   - -----------

    5                           5                                  5                      5

Thus we got John time as 81 /5 seconds .

Converting Savanna's time in fraction , we get

 19 8

----------  seconds .

  10  

We have two fractions with different denominator .

One is having denominator 5 and another is having denominator 10 .

We need to make the denominator same of both the fraction .

We need to make denominator 10 .

Multiply John fraction by 2 in both numerator and denominator by 2 to make denominator 10 .

81 * 2               162

----------  =      ------------ seconds .

5 *  2                   10

John is taking less time than Savanna . Thus John is faster .

Difference

198          162            36

-------  -     -------     =  ------- seconds  

10              10              10

Thus John is faster by  (36/10 ) seconds  =  3.6 seconds.

4 0
2 years ago
What is the surface area of a conical grain storage tank that has a height of 37 meters and a diameter of 16 meters? Round the a
jek_recluse [69]
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The lateral area of a cone is equal to πrl, where r = radius and l = slant height.
πrl = π(8)(√1433) ≈ 951.39958
(there are other formulas which do the same thing, but it doesn't matter.)

Now we add the lateral area and base together to find our surface area.
201.06193 + 951.39958 = 1152.46151 which rounds to C. 1,152 m².
8 0
3 years ago
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