2. Simplify the expression. (1 point)

x3 - 5

Step-by-step explanation:

Step  1  :

Trying to factor as a Difference of Cubes:

1.1      Factoring:  x3-5

Theory : A difference of two perfect cubes,  a3 - b3 can be factored into

             (a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =

           a3+a2b+ab2-ba2-b2a-b3 =

           a3+(a2b-ba2)+(ab2-b2a)-b3 =

           a3+0+0+b3 =

           a3+b3

Check :  5  is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Polynomial Roots Calculator :

1.2    Find roots (zeroes) of :       F(x) = x3-5

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        -130.00    

     1       1        1.00        -4.00    

     5       1        5.00        120.00    

Polynomial Roots Calculator found no rational roots

Final result :

 x3 - 5

Processing ends successfull

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594 square inches

step-by-step explanation:

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