Question

Factorise x cube + x square - 24

Answer 1

Answer:

Step-by-step explanation:

x3+x2-24  

Final result :

 x3 + x2 - 24

Step by step solution :

Step  1  :

Polynomial Roots Calculator :

1.1    Find roots (zeroes) of :       F(x) = x3+x2-24

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  -24.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,3 ,4 ,6 ,8 ,12 ,24

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -24.00      

     -2       1        -2.00        -28.00      

     -3       1        -3.00        -42.00      

     -4       1        -4.00        -72.00      

     -6       1        -6.00        -204.00      

     -8       1        -8.00        -472.00      

     -12       1       -12.00       -1608.00      

     -24       1       -24.00       -13272.00      

     1       1        1.00        -22.00      

     2       1        2.00        -12.00      

     3       1        3.00        12.00      

     4       1        4.00        56.00      

     6       1        6.00        228.00      

     8       1        8.00        552.00      

     12       1        12.00        1848.00      

     24       1        24.00       14376.00      

Polynomial Roots Calculator found no rational roots

Final result :

 x3 + x2 - 24