Factors completely x² + 16?
(x + 4)(x + 4); (x + 4)(x - 4), prime, (x - 4)(x - 4)

Solution:

Let us try to find out the roots of the equation x² + 16 using the quadratic formula x = [ - b ± √ b² - 4ac ] / 2a.

Step 1: Express the polynomial in the form of quadratic equation a² + bx + c = 0

x² + 0x + 16 = 0

Step 2: Find the roots using quadratic formula x = [ - b ± √ b² - 4ac ] / 2a.

Where a = 1 coefficient of x², b = 0 coefficient of x, c = 16 constant term.

x = [0 ± √ - 4(1)(16)] /2

x = ( ± √- 64) /2

x = (± 8i) /2

x = -4i and x = 4i

The above polynomial has complex roots.

A prime polynomial is a polynomial which can not be factored into polynomial of lower degrees and can not factorised with rational numbers..

Thus, the equation is a prime polynomial.

Factors completely x2 + 16?.
(x + 4)(x + 4); (x + 4)(x - 4), prime, (x - 4)(x - 4)

Summary:

The factor of x² + 16 is x2 + 16 as the equation is a prime polynomial and it has complex roots.