Question

question
factor completely.
$5x^2 + 9x + 4$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times4 = 20\) and add up to \(9\). The numbers are \(5\) and \(4\) since \(5\times4 = 20\) and \(5 + 4=9\).

Step2: Split the middle term

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

Step3: Group and factor

Group the first two terms and the last two terms:
\((5x^{2}+5x)+(4x + 4)\)
Factor out the greatest common factor from each group:
\(5x(x + 1)+4(x + 1)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((x + 1)\):
\((5x + 4)(x + 1)\)

Answer:

\((5x + 4)(x + 1)\)