Question

Use factoring to solve the polynomial 6x⁴-24x²=0

Answer 1

The polynomial 6x⁴-24x²=0 is factored by first factoring out the greatest common factor, 6x², and then recognizing that the remaining term is a difference of squares. This leads to solutions x=0, x=-2, and x=2.

Step-by-step explanation:

To solve the polynomial 6x⁴-24x²=0, we need to factor it. Factoring allows us to break down the equation into simpler terms that can be set to zero, giving us the potential solutions. Here are the steps to factor and solve the polynomial:

1. Factor out the greatest common factor (GCF), which is 6x² in this case.
2. This gives us 6x²(x²-4)=0.
3. Now recognize that x²-4 is a difference of squares and can be factored further into (x+2)(x-2).
4. Therefore, we have 6x²(x+2)(x-2)=0.
5. Set each factor equal to zero and solve for x: x=0, x=-2, and x=2.

Thus, the solutions to the polynomial are x=0, x=-2, and x=2.