Question

2x² - 13x - 24 = □

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times(-24)= - 48\) and add up to \(-13\). The numbers are \(-16\) and \(3\) since \(-16\times3=-48\) and \(-16 + 3=-13\).

Step2: Rewrite the middle term

Rewrite \(-13x\) as \(-16x+3x\) in the quadratic expression:
\(2x^{2}-16x + 3x-24\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((2x^{2}-16x)+(3x - 24)\)
Factor out the greatest common factor from each group:
\(2x(x - 8)+3(x - 8)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((x - 8)\):
\((2x + 3)(x - 8)\)

Answer:

\((2x + 3)(x - 8)\)