Which expression represents the polynomial −7x+x3−6+x2 rewritten in standard form? x3−5x+6 x2−7x−6 x3−2x2−7x−6 x3+x2−7x−6 x3−7x+6

the answer is  x3 + x2 - 7x - 6

step by step explanation

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

Step by step solution :

Step  1  :

Checking for a perfect cube :

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

Trying to factor by pulling out :

1.2      Factoring:  x3+x2-7x-6

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

Group 1:  -7x-6

Group 2:  x3+x2

Pull out from each group separately :

Group 1:   (7x+6) • (-1)

Group 2:   (x+1) • (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 :

1.3    Find roots (zeroes) of :       F(x) = x3+x2-7x-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

Let us test

   P      Q      P/Q      F(P/Q)      Divisor

      -1         1          -1.00          1.00      

      -2         1          -2.00          4.00      

      -3         1          -3.00          -3.00      

      -6         1          -6.00          -144.00      

      1         1          1.00          -11.00      

      2         1          2.00          -8.00      

      3         1          3.00          9.00      

      6         1          6.00          204.00      

Polynomial Roots Calculator found no rational roots

Final result :

 x3 + x2 - 7x - 6

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