Question

factor the expression completely.

(2x^2 + 10x - 12)

(2(x - 6)(x + 1))
(2(x + 6)(x - 1))
(2(x - 2)(x - 3))
(2(x + 2)(x + 3))

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Factor out the greatest common factor (GCF)

Identify the GCF of the terms in the expression \( 2x^2 + 10x - 12 \). The GCF is \( 2 \).

$$ 2(x^2 + 5x - 6) $$

Step 2: Factor the remaining trinomial

Find two numbers that multiply to \( -6 \) and add to \( 5 \).

• The factors are \( 6 \) and \( -1 \) because:

$$ 6 \cdot (-1) = -6 $$

$$ 6 + (-1) = 5 $$

Write the factored form of the trinomial:

$$ 2(x + 6)(x - 1) $$

Answer:

\( 2(x + 6)(x - 1) \) (the second option)