Question

What is the solution of the inequality x^3 + 3x^2 > 7x + 6

Answer 1

Answer:

Equation at the end of step 1

 (((x3) +  3x2) -  7x) -  6

STEP

2

:

Checking for a perfect cube

2.1    x3+3x2-7x-6  is not a perfect cube

Trying to factor by pulling out :

2.2      Factoring:  x3+3x2-7x-6  

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

Group 1:  -7x-6  

Group 2:  x3+3x2  

Pull out from each group separately :

Group 1:   (7x+6) • (-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+3x2-7x-6

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  -6.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,3 ,6

Answer 2

Answer: 54

Step-by-step explanation: