Question

completely factor the trinomial, if possible.

\\16x^3 + 24x^2 + 8x\\

Explanation:

Find the greatest common factor

Using the Factoring Polynomials by GCF knowledge point

$$ \text{GCF}(16x^3, 24x^2, 8x) = 8x $$

Factor out the GCF

Using the Factoring Polynomials by GCF knowledge point

$$ 16x^3 + 24x^2 + 8x = 8x(2x^2 + 3x + 1) $$

Factor the remaining trinomial

Using the Factoring Trinomials knowledge point

$$ 2x^2 + 3x + 1 = (2x + 1)(x + 1) $$

Write the completely factored expression

Using the Factoring Trinomials knowledge point

$$ 16x^3 + 24x^2 + 8x = 8x(2x + 1)(x + 1) $$

Answer:

\(8x(2x + 1)(x + 1)\)