Question

Factor the polynomial expression 3x² + 2.

A. (√3x + √2i)(√3x - √/2i)
B. (3x + √2i)(3x - √2i)
C. (√3x + √2)(√3x - √2)
D. (√3x + i)(√√3x - i)

Answer 1

`\boxed{\left(x+i\sqrt{(2)/(3)}i \right)\left(x-i\sqrt{(2)/(3)}i \right)}`

Explanation:

Setting the expression equal to zero to find the roots,

`3x^2 +2=0\\\\3x^2 =-2\\\\x^2 =-(2)/(3)\\\\x=\pm i\sqrt{(2)/(3)}`

This means that

`3x^2 +2=\boxed{\left(x+i\sqrt{(2)/(3)}i \right)\left(x-i\sqrt{(2)/(3)}i \right)}`