Question

Divide 2x³-3x²+5x-7 by x-2​

Answer 1

Answer: p(1/2)=11/2p(a)=a.

Step-by-step explanation:

Answer 2

Answer:

       2x3 - 5x2 + 2x - 7

 ——————————————————

       x - 2      

Step-by-step explanation:            2x3 - 5x2 + 2x - 7

Simplify   ——————————————————

                 x - 2      

Checking for a perfect cube :

3.1    2x3 - 5x2 + 2x - 7  is not a perfect cube

Trying to factor by pulling out :

3.2      Factoring:  2x3 - 5x2 + 2x - 7

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

Group 1:  2x - 7

Group 2:  2x3 - 5x2

Pull out from each group separately :

Group 1:   (2x - 7) • (1)

Group 2:   (2x - 5) • (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) = 2x3 - 5x2 + 2x - 7

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  2  and the Trailing Constant is  -7.

The factor(s) are:

of the Leading Coefficient :  1,2

of the Trailing Constant :  1 ,7

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -16.00    

     -1       2        -0.50        -9.50    

     -7       1        -7.00        -952.00    

     -7       2        -3.50        -161.00    

     1       1        1.00        -8.00    

     1       2        0.50        -7.00    

     7       1        7.00        448.00    

     7       2        3.50        24.50    

Polynomial Roots Calculator found no rational roots

Polynomial Long Division :

3.4    Polynomial Long Division

Dividing :  2x3 - 5x2 + 2x - 7

                             ("Dividend")

By         :    x - 2    ("Divisor")

dividend     2x3  -  5x2  +  2x  -  7

- divisor  * 2x2     2x3  -  4x2        

remainder      -  x2  +  2x  -  7

- divisor  * -x1      -  x2  +  2x    

remainder              -  7

- divisor  * 0x0                

remainder              -  7

Quotient :  2x2 - x

Remainder :  -7

so x=-7