Question

which expression is the completely factored form of the expression (x^2 - 3x - 28)?

(a) ((x - 7)(x + 4))
(b) ((x + 7)(x - 4))
(c) ((x + 14)(x - 2))
(d) ((x + 14)(x + 2))

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Identify coefficients

For the quadratic expression \(x^2 - 3x - 28\):

$$a = 1, \quad b = -3, \quad c = -28$$

Step 2: Find factors

Find two numbers that multiply to \(c = -28\) and add to \(b = -3\):

$$-7 \cdot 4 = -28$$

$$-7 + 4 = -3$$

Step 3: Write factored form

$$(x - 7)(x + 4)$$

Answer:

\((x - 7)(x + 4)\)