Question

completely factor the trinomial, if possible.

\\2x^2 + 20x + 48\\

Explanation:

Factor out the greatest common factor

Using the Factoring Polynomials by GCF knowledge point, we identify the greatest common factor of the terms in the trinomial \(2x^2 + 20x + 48\).
The coefficients are \(2\), \(20\), and \(48\). Their greatest common divisor is \(2\).
We factor out \(2\):

$$2x^2 + 20x + 48 = 2(x^2 + 10x + 24)$$

Factor the remaining quadratic trinomial

Using the Factoring Trinomials knowledge point, we factor the quadratic expression \(x^2 + 10x + 24\).
We look for two integers whose product is \(24\) and whose sum is \(10\).
These integers are \(6\) and \(4\) because:

$$6 \cdot 4 = 24$$

$$6 + 4 = 10$$

Thus, we write:

$$x^2 + 10x + 24 = (x + 6)(x + 4)$$

Write the completely factored expression

We combine the factored parts to write the final completely factored expression:

$$2(x + 6)(x + 4)$$

Answer:

\(2(x + 6)(x + 4)\)