Place the indicated product in the proper location on the grid. (x2 + 4)(x2 - 4)

 (x2 + 4) • (x + 2) • (x - 2)

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  :

Polynomial Roots Calculator :

1.1    Find roots (zeroes) of :       F(x) = x2+4

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  4.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,4

Let us test

 P    Q    P/Q    F(P/Q)    Divisor

     -1       1        -1.00        5.00    

     -2       1        -2.00        8.00    

     -4       1        -4.00        20.00    

     1       1        1.00        5.00    

     2       1        2.00        8.00    

     4       1        4.00        20.00    

Polynomial Roots Calculator found no rational roots

Trying to factor as a Difference of Squares :

1.2      Factoring:  x2-4

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 : 4 is the square of 2

Check :  x2  is the square of  x1

Factorization is :       (x + 2)  •  (x - 2)

Final result :

 (x2 + 4) • (x + 2) • (x - 2)

Step-by-step explanation:

the answer is x^4-16

Step-by-step explanation:

it is b)

hope this : )

step-by-step explanation: