Question

question
factor completely:
$5x^2 - 4x - 9$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times(-9)= -45\) and add up to \(-4\). The numbers are \(-9\) and \(5\) since \(-9\times5 = -45\) and \(-9 + 5=-4\).

Step2: Rewrite the middle term

Rewrite \(-4x\) as \(-9x + 5x\) in the expression \(5x^{2}-4x - 9\):
\(5x^{2}-9x + 5x-9\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((5x^{2}-9x)+(5x - 9)\)
Factor out the greatest common factor from each group:
\(x(5x - 9)+1(5x - 9)\)

Step4: Factor out the common binomial

Factor out the common binomial \((5x - 9)\):
\((x + 1)(5x - 9)\)

Answer:

\((x + 1)(5x - 9)\)