Question

Factorise x^3-3x^2-3x-5

Answer 1

Step by step solution :

Step  1  :

Equation at the end of step  1  :

(((x3) - 3x2) - 3x) - 5 = 0

Step  2  :

Checking for a perfect cube :

 2.1    x3-3x2-3x-5  is not a perfect cube 

Trying to factor by pulling out :

 2.2      Factoring:  x3-3x2-3x-5 

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

Group 1:  -3x-5 
Group 2:  -3x2+x3 

Pull out from each group separately :

Group 1:   (3x+5) • (-1)
Group 2:   (x-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 :

 2.3    Find roots (zeroes) of :       F(x) = x3-3x2-3x-5
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  -5. 

 The factor(s) are: 

of the Leading Coefficient :  1
 of the Trailing Constant :  1 ,5 

 Let us test ....

  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      -6.00        -5     1      -5.00      -190.00        1     1      1.00      -10.00        5     1      5.00      30.00   


Polynomial Roots Calculator found no rational roots

Equation at the end of step  2  :

x3 - 3x2 - 3x - 5 = 0

Step  3  :

Cubic Equations :

 3.1     Solve   x3-3x2-3x-5 = 0

Future releases of Tiger-Algebra will solve equations of the third degree directly.

Meanwhile we will use the Bisection method to approximate one real solution.

Approximating a root using the Bisection Method :

We now use the Bisection Method to approximate one of the solutions. The Bisection Method is an iterative procedure to approximate a root (Root is another name for a solution of an equation).

The function is   F(x) = x3 - 3x2 - 3x - 5

At   x=   4.00   F(x)  is equal to  -1.00 
At   x=   5.00   F(x)  is equal to  30.00 

Intuitively we feel, and justly so, that since  F(x) is negative on one side of the interval, andpositive on the other side then, somewhere inside this interval,  F(x)  is zero 

Procedure :
(1) Find a point "Left" where F(Left) < 0

(2) Find a point 'Right' where F(Right) > 0

(3) Compute 'Middle' the middle point of the interval [Left,Right]

(4) Calculate Value = F(Middle)

(5) If Value is close enough to zero goto Step (7)

Else :  
If Value < 0 then : Left <- Middle
If Value > 0 then : Right <- Middle

(6) Loop back to Step (3)

(7) Done!! The approximation found is Middle

Follow Middle movements to understand how it works : 

Left Value(Left) Right Value(Right) 4.000000000 -1.000000000 5.000000000 30.000000000 0.000000000 -5.000000000 5.000000000 30.000000000 2.500000000 -15.625000000 5.000000000 30.000000000 3.750000000 -5.703125000 5.000000000 30.000000000 3.750000000 -5.703125000 4.375000000 8.193359375 3.750000000 -5.703125000 4.062500000 0.347900391 3.906250000 -2.890472412 4.062500000 0.347900391 3.984375000 -1.325931549 4.062500000 0.347900391 4.023437500 -0.502855778 4.062500000 0.347900391 4.042968750 -0.080960095 4.062500000 0.347900391 4.042968750 -0.080960095 4.052734375 0.132596754 4.042968750 -0.080960095 4.047851563 0.025600330 4.045410156 -0.027734339 4.047851563 0.025600330 4.046630859 -0.001080624 4.047851563 0.025600330 4.046630859 -0.001080624 4.047241211 0.012256448 4.046630859 -0.001080624 4.046936035 0.005587061 4.046630859 -0.001080624 4.046783447 0.002253006 4.046630859 -0.001080624 4.046707153 0.000586138 4.046669006 -0.000247256 4.046707153 0.000586138 4.046669006 -0.000247256 4.046688080 0.000169437 4.046678543 -0.000038910 4.046688080 0.000169437 4.046678543 -0.000038910 4.046683311 0.000065263 4.046678543 -0.000038910 4.046680927 0.000013176


     Next Middle will get us close enough to zero: 

     F(  4.046680331 ) is   0.000000155  

     The desired approximation of the solution is: 

       x ≓ 4.046680331 

     Note, ≓ is the approximation symbol 

One solution was found :

                         x ≓ 4.046680331
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Answer 2

Answer:

i may be not sure the answer but i can explain the steps

Step-by-step explanation:first fine the x for example

p(1)=x^3-3x^2-9x-5

you will not get zero

find p as any number until you get value zero  i got the zero p(-1) so x+1 is the factor of the question

now

step 3

divide x+1 by the question  u will get x^2-4x-5 is the quotient

and after that yuou can factorize

im sorry i could n find the answer but these are  steps u should start thank you pls follow me