If j(x) = x4 - 81, and k(x) = x + 3 then j(x) k(x) =

 1.1      Factoring:  x4-81 

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 : 81 is the square of 9
Check :  x4  is the square of  x2 

Factorization is :       (x2 + 9)  •  (x2 - 9) 

 1.2    Find roots (zeroes) of :       F(x) = x2 + 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  1  and the Trailing Constant is  9. 

 The factor(s) are: 

of the Leading Coefficient :  1
 of the Trailing Constant :  1 ,3 ,9 

 Let us test

Polynomial Roots Calculator found no rational roots

 1.3      Factoring:  x2 - 9 

Check : 9 is the square of 3
Check :  x2  is the square of  x1 

Factorization is :       (x + 3)  •  (x - 3) 

plz yuo

step-by-step explanation: