Question

How to factorise X^3-2x^2-2X-3 by step by step method

Answer 1

 x3-2x2-2x-3 Final result : (x2 + x + 1) • (x - 3)

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

Step by step solution :Step  1  :Equation at the end of step  1  : (((x3) - 2x2) - 2x) - 3 Step  2  :Checking for a perfect cube :

 2.1    x3-2x2-2x-3  is not a perfect cube 

Trying to factor by pulling out :

 2.2      Factoring:  x3-2x2-2x-3 

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

Group 1:  -2x-3 
Group 2:  -2x2+x3 

Pull out from each group separately :

Group 1:   (2x+3) • (-1)
Group 2:   (x-2) • (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 :

 2.3    Find roots (zeroes) of :       F(x) = x3-2x2-2x-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  1  and the Trailing Constant is  -3. 

 The factor(s) are: 

of the Leading Coefficient :  1
 of the Trailing Constant :  1 ,3 

 Let us test ....

  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      -4.00        -3     1      -3.00      -42.00        1     1      1.00      -6.00        3     1      3.00      0.00    x-3 

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 
   x3-2x2-2x-3 
can be divided with  x-3 

Polynomial Long Division :

 2.4    Polynomial Long Division 
Dividing :  x3-2x2-2x-3 
                              ("Dividend")
By         :    x-3    ("Divisor")

dividend  x3 - 2x2 - 2x - 3 - divisor * x2   x3 - 3x2     remainder    x2 - 2x - 3 - divisor * x1     x2 - 3x   remainder      x - 3 - divisor * x0       x - 3 remainder       0

Quotient :  x2+x+1  Remainder:  0 

Trying to factor by splitting the middle term

 2.5     Factoring  x2+x+1 

The first term is,  x2  its coefficient is  1 .
The middle term is,  +x  its coefficient is  1 .
The last term, "the constant", is  +1 

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

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

     -1   +   -1   =   -2     1   +   1   =   2

Observation : No two such factors can be found !! 
Conclusion : Trinomial can not be factored

Final result : (x2 + x + 1) • (x - 3)

Answer 2

Answer:

sorry i don't know how to solve this is other way