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a\left(3x^{2}+2\right)+b\left(3x^{2}+2\right)
Do the grouping 3ax^{2}+2b+3bx^{2}+2a=\left(3ax^{2}+2a\right)+\left(3bx^{2}+2b\right), and factor out a in the first and b in the second group.
\left(3x^{2}+2\right)\left(a+b\right)
Factor out common term 3x^{2}+2 by using distributive property. Polynomial 3x^{2}+2 is not factored since it does not have any rational roots.