Question

Write the quadratic as a product of factors irreducible over the reals. x2 + 16

Answer 1

A2 + B2 = (A + Bi)(A – Bi) so the answer is (x + 4i)(x - 4i)

Answer 2

The product of factors irreducible over the reals are
`x^2+16=(x+4i)(x-4i)`

Explanation:

Given : Quadratic form
`x^2+16`

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.

`x^2+16=0`

`x^2=-16`

Root both side,

`√(x^2)=√(-16)`

`x=\pm 4i`

So,The factors of the quadratic equation is
`(x+4i)(x-4i)` in the form of complex number.

Therefore, The product of factors irreducible over the reals are
`x^2+16=(x+4i)(x-4i)`