Answer:
The product of factors irreducible over the reals are [tex]x^2+16=(x+4i)(x-4i)[/tex]
Step-by-step explanation:
Given : Quadratic form [tex]x^2+16[/tex]
To find : Write the quadratic as a product of factors irreducible over the reals?
Solution :
To find the product first we have to find the roots of the quadratic.
[tex]x^2+16=0[/tex]
[tex]x^2=-16[/tex]
Root both side,
[tex]\sqrt{x^2}=\sqrt{-16}[/tex]
[tex]x=\pm 4i[/tex]
So,The factors of the quadratic equation is [tex](x+4i)(x-4i)[/tex] in the form of complex number.
Therefore, The product of factors irreducible over the reals are [tex]x^2+16=(x+4i)(x-4i)[/tex]
