Question

Which of the following shows the factorization of 3x⁴ + 6x³ + 4x² + 8x?

1) x(3x² + 4)(x²)
2) x(3x² + 4)(x - 2)
3) (3x² + 4)(x²)
4) x(3x² + 4)(x²)

Answer 1

The factorization of 3x⁴ + 6x³ + 4x² + 8x is x(3x² + 4)(x²).

Step-by-step explanation:

The factorization of 3x⁴ + 6x³ + 4x² + 8x is given by option 4) x(3x² + 4)(x²).

To factorize the expression, we look for common factors. We can first factor out x, giving us:

x(3x³ + 4x² + 8)

Now, we need to factor the trinomial 3x³ + 4x² + 8. This trinomial does not have any common factors that can be factored out, so we cannot simplify it further. Therefore, the factorization of 3x⁴ + 6x³ + 4x² + 8x is x(3x² + 4)(x²).