Question

Factor the polynomial expression 4x2 +9.

Answer 1

Answer:

Step-by-step 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:

$x^2=-\frac{9}{4}$ Then take the square root of both sides:

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

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

x = ±$\sqrt{i^2*\frac{9}{4} }$

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

x = ±$\frac{3}{2}i$

And there you go!