Question

(8x3 - 30x + 21) / (4x -6)

Answer 1

Answer:

$\frac{ {8x}^{3} - 30x + 21 }{2(2x - 3)}$

Step-by-step explanation:

1) Factor out the common terms 2.

$\frac{8x^{3} - 30x + 21}{2(2x - 3)}$

Therefor, the answer is 8x³ - 30x + 21 / 2 ( 2x - 3 ).

Answer 2

Answer:

 8x3 - 30x + 21

————————

   2 • (2x - 3)

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "x3"   was replaced by   "x^3".

                   8x3 - 30x + 21

Simplify   —————————

                         4x - 6  

Pull out like factors :

  4x - 6  =   2 • (2x - 3)

Find roots (zeroes) of :       F(x) = 8x3 - 30x + 21

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  8  and the Trailing Constant is  21.

The factor(s) are:

of the Leading Coefficient :  1,2 ,4 ,8

of the Trailing Constant :  1 ,3 ,7 ,21

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        43.00    

     -1       2        -0.50        35.00    

     -1       4        -0.25        28.38    

     -1       8        -0.12        24.73    

     -3       1        -3.00        -105.00    

Note - For tidiness, printing of 27 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Polynomial Long Division

Dividing :  8x3 - 30x + 21

                             ("Dividend")

By         :    2x - 3    ("Divisor")

dividend     8x3      -  30x  +  21

- divisor  * 4x2     8x3  -  12x2        

remainder         12x2  -  30x  +  21

- divisor  * 6x1         12x2  -  18x    

remainder          -  12x  +  21

- divisor  * -6x0          -  12x  +  18

remainder                 3

Quotient :  4x2 + 6x - 6

Remainder :  3

Answer:        8x3 - 30x + 21

                    ————————

                        2 • (2x - 3)