Solve 6x^6-9x^4=0: Common Factor Factoring Practice

Look at both coefficients and variables separately. For $6x^6-9x^4$: GCF of 6 and 9 is 3, and GCF of $x^6$ and $x^4$ is $x^4$. So the overall GCF is $3x^4$.

When you factor out $3x^4$, you get $3x^4(2x^2-3)=0$. Since $3x^4 = 0$ when $x = 0$, zero is always a solution when you factor out variables!

Set each factor equal to zero. After factoring out $3x^4$, solve $2x^2-3=0$ by adding 3 to both sides, then dividing by 2: $x^2 = \frac{3}{2}$, so $x = \pm\sqrt{\frac{3}{2}}$.

Yes! $\sqrt{\frac{3}{2}}$ can be written as $\frac{\sqrt{6}}{2}$ by rationalizing. Both forms are correct, but some teachers prefer one over the other.

Each factor must equal zero for the entire product to equal zero. This is the zero product property. Don't solve just one factor - you'll miss solutions!