19x^2+7-[3(x^2-7)+9]
how do you simplify

 1.1      Factoring:  x2-7 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 = 
         A2 - B2

Note :  AB = BA is the commutative property of multiplication. 

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 7 is not a square !! 

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

 4.1     Pull out like factors :

   16x2 + 18  =   2 • (8x2 + 9) 

 4.2    Find roots (zeroes) of :       F(x) = 8x2 + 9
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  8  and the Trailing Constant is  9. 

 The factor(s) are: 

of the Leading Coefficient :  1,2 ,4 ,8 
 of the Trailing Constant :  1 ,3 ,9 

 Let us test

Note - For tidiness, printing of 19 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

b

step-by-step explanation: