Solve (3-x^2)+(2abx^2-6ab)

$$( 3 - x ^ { 2 } ) + ( 2 a b x ^ { 2 } - 6 a b )$$

Factor

$$\left(x^{2}-3\right)\left(2ab-1\right)$$

Solution Steps

Do the grouping 3-x^{2}+2abx^{2}-6ab=\left(3-x^{2}\right)+\left(2abx^{2}-6ab\right), and factor out -1 in the first and 2ab in the second group.

$$-\left(x^{2}-3\right)+2ab\left(x^{2}-3\right)$$

Factor out common term x^{2}-3 by using distributive property. Polynomial x^{2}-3 is not factored since it does not have any rational roots.

$$\left(x^{2}-3\right)\left(-1+2ab\right)$$

Evaluate

$$\left(x^{2}-3\right)\left(2ab-1\right)$$