Question

factor the expression completely.

(x^2 - 5x - 6)

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

Explanation:

🆕 New Concept Discovered: Factoring Trinomials
Finding two numbers that multiply to the constant and add to the middle coefficient.

Step 1: Identify the coefficients

We need to factor the quadratic expression:

$$ x^2 - 5x - 6 $$

Here, the coefficients are:

• Product (\(a \cdot c\)) = \(-6\)
• Sum (\(b\)) = \(-5\)

Step 2: Find the factors

We look for two numbers that multiply to \(-6\) and add up to \(-5\).

Let's list the factor pairs of \(-6\):

• \(1\) and \(-6\) (Sum: \(1 + (-6) = -5\))
• \(-1\) and \(6\) (Sum: \(-1 + 6 = 5\))
• \(2\) and \(-3\) (Sum: \(2 + (-3) = -1\))
• \(-2\) and \(3\) (Sum: \(-2 + 3 = 1\))

The pair that works is \(1\) and \(-6\).

Step 3: Write the factored form

Using the factors \(1\) and \(-6\), we write the expression as:

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

Answer:

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