Question

Factor the polynomial expression 4x2 +9.

Answer 1

Explanation:

Factor it by first setting it equal to 0:

`4x^2+9=0` Now subtract 9 from both sides:

`4x^2=-9` Divide both sides by 4:

`x^2=-(9)/(4)` Then take the square root of both sides:

x = ±
`\sqrt{-(9)/(4) }` , which of course is not allowed. Therefore, we have to allow for the imaginary numbers in this solution. Knowing that,

x = ±
`\sqrt{-1*(9)/(4) }` is an equivalent radicand, we can now replace -1 with its imaginary counterpart:

x = ±
`\sqrt{i^2*(9)/(4) }`

Each one of the elements in the radicand are perfect squares, so we simplify as follows:

x = ±
`(3)/(2)i`

And there you go!