Factor the polynomial x^2-5x-24. Your answer can b

Questions: Factor the polynomial x^2-5x-24. Your answer can be written as (x+A)(x+B) where A<B

Transcript text: Factor the polynomial $x^{2}-5 x-24$. Your answer can be written as $(x+A)(x+B)$ where $A

Solution

Solution Steps

To factor the polynomial $x^2 - 5x - 24$, we need to find two numbers whose product is the constant term (-24) and whose sum is the linear coefficient (-5). Once these numbers are identified, they can be used to express the polynomial in its factored form $(x + A)(x + B)$.

Step 1: Identify the Polynomial

We start with the polynomial $x^2 - 5x - 24$.

Step 2: Factor the Polynomial

To factor the polynomial, we look for two numbers that multiply to $-24$ (the constant term) and add up to $-5$ (the coefficient of $x$). The numbers that satisfy these conditions are $-8$ and $3$.

Step 3: Write the Factored Form

Using the identified numbers, we can express the polynomial in its factored form: \[ x^2 - 5x - 24 = (x - 8)(x + 3) \]