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)