Question

factor $2x^2 - 9x - 5$.

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times(-5)= -10\) and add up to \(-9\). The numbers are \(-10\) and \(1\) since \(-10\times1 = -10\) and \(-10 + 1=-9\).

Step2: Rewrite the middle term

Rewrite \(-9x\) as \(-10x+x\) in the expression \(2x^{2}-9x - 5\):
\[2x^{2}-10x+x - 5\]

Step3: Group and factor

Group the first two terms and the last two terms:
\((2x^{2}-10x)+(x - 5)\)
Factor out the greatest common factor from each group:
\(2x(x - 5)+1(x - 5)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((x - 5)\):
\((2x + 1)(x - 5)\)

Answer:

\((2x + 1)(x - 5)\)