question\nfactor.\n$x^2 - 3x - 28$

Answer

Explanation:

Step1: Find two numbers

We need two numbers that multiply to $-28$ (the constant term) and add up to $-3$ (the coefficient of $x$). Let's list the factor pairs of $-28$:

$1$ and $-28$: $1 + (-28) = -27$
$2$ and $-14$: $2 + (-14) = -12$
$4$ and $-7$: $4 + (-7) = -3$ (This works!)

Step2: Factor the quadratic

Using the two numbers $4$ and $-7$, we can factor the quadratic $x^2 - 3x - 28$ as $(x + 4)(x - 7)$. We check: $$(x + 4)(x - 7) = x^2 - 7x + 4x - 28 = x^2 - 3x - 28$$ (Which matches the original expression)

Answer:

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