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

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

step-by-step explanation:

the height of the surface increases from the center out to the sides of the road.

step-by-step explanation:

as we move out we move away from the x-axis.

and as mentioned in the problem statement that height of a road increases when we move away from the center x.

hence proved that 3rd option

the height of the surface increases from the center out to the sides of the road.

is the correct option.