What is the quotient when 10x^3-3x^2-7x+3 is divided by 2x-1?

Answers

Answer 1

Answer:

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 

STEP  

2

:

Equation at the end of step

2

:

 

STEP

3

:

           10x3 - 3x2 - 7x + 3

Simplify   ———————————————————

                 2x - 1        

Checking for a perfect cube :

3.1    10x3 - 3x2 - 7x + 3  is not a perfect cube

Trying to factor by pulling out :

3.2      Factoring:  10x3 - 3x2 - 7x + 3  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -7x + 3  

Group 2:  10x3 - 3x2  

Pull out from each group separately :

Group 1:   (-7x + 3) • (1) = (7x - 3) • (-1)

Group 2:   (10x - 3) • (x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

3.3    Find roots (zeroes) of :       F(x) = 10x3 - 3x2 - 7x + 3

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  10  and the Trailing Constant is  3.

The factor(s) are:

of the Leading Coefficient :  1,2 ,5 ,10

of the Trailing Constant :  1 ,3

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -3.00      

     -1       2        -0.50        4.50      

     -1       5        -0.20        4.20      

     -1       10        -0.10        3.66      

     -3       1        -3.00        -273.00      

     -3       2        -1.50        -27.00      

     -3       5        -0.60        3.96      

     -3       10        -0.30        4.56      

     1       1        1.00        3.00      

     1       2        0.50        0.00      2x - 1  

     1       5        0.20        1.56      

     1       10        0.10        2.28      

     3       1        3.00        225.00      

     3       2        1.50        19.50      

     3       5        0.60        -0.12      

     3       10        0.30        0.90      

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

  10x3 - 3x2 - 7x + 3  

can be divided with  2x - 1  

Polynomial Long Division :

3.4    Polynomial Long Division

Dividing :  10x3 - 3x2 - 7x + 3  

                             ("Dividend")

By         :    2x - 1    ("Divisor")

dividend     10x3  -  3x2  -  7x  +  3  

- divisor  * 5x2     10x3  -  5x2          

remainder         2x2  -  7x  +  3  

- divisor  * x1         2x2  -  x      

remainder          -  6x  +  3  

- divisor  * -3x0          -  6x  +  3  

remainder                0

Quotient :  5x2+x-3  Remainder:  0  

Trying to factor by splitting the middle term

3.5     Factoring  5x2+x-3  

The first term is,  5x2  its coefficient is  5 .

The middle term is,  +x  its coefficient is  1 .

The last term, "the constant", is  -3  

Step-1 : Multiply the coefficient of the first term by the constant   5 • -3 = -15  

Step-2 : Find two factors of  -15  whose sum equals the coefficient of the middle term, which is   1 .

     -15    +    1    =    -14  

     -5    +    3    =    -2  

     -3    +    5    =    2  

     -1    +    15    =    14  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Canceling Out :

3.6    Cancel out  (2x-1)  which appears on both sides of the fraction line.

Final result :

 5x2 + x - 3

Answer 2

The quotient when 10x³-3x²-7x+3 divided by 2x-1 is -21/8.

To calculate the quotient of the equation 10x³-3x²-7x+3 when it is divided by 2x-1, we use the quotient theorem.

Remainder theorem

The quotient theorem states that if f(x) is divided by x-a, then the remainder is f(a).

From the question,

Given:

f(x) = 10x³-3x²-7x+3............. Equation 1diveded by 2x-1

The quotient is f(1/2), we substitute the value of x as 1/2 into equation 1

f(1/2) = 10(1/2)³-3(1/2)²-7(1/2)+3f(1/2) = (10/8)-(3/4)-(7/2)+3f(1/2) = -21/8

Hence, The quotient when 10x³-3x²-7x+3 divided by 2x-1 is -21/8.

Learn more about the quotient theorem here: https://brainly.com/question/13328536

#SPJ2


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Step-by-step explanation:

Answer:

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Answer:

Step-by-step explanation:

Because bed is rectangular and diagonal is dividing it into two right angled Δs , we are using Pythagorean Theorem c² = a² + b²

c² = 57² + 76²

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Explanation:

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Answers

Answer:

B.Andrew will have 0 points

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Answers

Qualitative is something that describe like the different colors of something.

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Answers

Answer:

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what will he have to pay? (Round your answer to the nearest cent.)

$

Answers

Answer: 1902.36

Step-by-step explanation:

When interest is compounded monthly , the formula to find the accumulated amount is

[tex]A=P(1+\dfrac{r}{12})^{12t}[/tex] , where P = principal value , r = rate of interest , t = time.

As per given,

r= 24% =  0.24

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Put all value in formula , we get

[tex]A= 1500(1+\dfrac{0.24}{12})^{12\times 1}\\\\=1500(1+0.02)^{12}\\\\=1500(1.02)^{12}\\\\=1500(1.26824179456)\approx1902.36[/tex]

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What are the three ways we can write ratios

Answers

Answer:

Step-by-step explanation:

The most common way to write a ratio is as a fraction, 3/6. We could also write it using the word "to," as "3 to 6." Finally, we could write this ratio using a colon between the two numbers, 3:6. Be sure you understand that these are all ways to write the same number.

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Considering example is 4 : 8

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Loan B (20 years) results in monthly payments of $268.66.

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Answers

Answer:

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Step-by-step explanation:

Loan A

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Please help fast! I need the answer along with step by steps explaining to I can learn it thanks I’ll give brainlist to who does it for me I appreciate it!

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Answer:

?

Step-by-step explanation:

Fuimos al Circo "Hermanos Poncho y Carlos", y tuvimos que pagar en total $350 por mis dos hermanos, mis padres y yo. Mi mamá pagó 1/7 parte del total, mi hermano mayor 2/5 del total y mi papá el resto. ¿Cuánto pagó mi papá?

Que operación necesito hacer plss ?​

Answers

Answer:

$160

Step-by-step explanation:

El monto total a pagar es de $350

[tex]\dfrac{1}{7}[/tex] es pagado por mamá

[tex]\dfrac{2}{5}[/tex] es pagado por el hermano mayor

La porción pagada por papá es

[tex]1-(\dfrac{1}{7}+\dfrac{2}{5})=1-(\dfrac{5+14}{35})\\ =1-\dfrac{19}{35}\\ =\dfrac{35-19}{35}\\ =\dfrac{16}{35}[/tex]

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Answers

Answer:

Option C is correct.

Step-by-step explanation:

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Answers

Answer:

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Answer:

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Answer:

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Step-by-step explanation:

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Answer:

4050

Step-by-step explanation:

Length

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Centimeter

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4050

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Answer:

Step-by-step explanation:

Some people just want to mess around

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frrrrr. ig bc there desperate lm.ao

Step-by-step explanation:

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Answers

Answer:

r = 2

Step-by-step explanation:

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its b

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

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Answer:

D. Cant be determined

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Answer:

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Step-by-step explanation:

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D

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can i have brainliest?

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