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.
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