Question

question
factor the trinomial:

$5x^2 + 28x + 15$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times15 = 75\) and add up to \(28\). The numbers are \(25\) and \(3\) since \(25\times3 = 75\) and \(25 + 3=28\).

Step2: Split the middle term

Rewrite the middle term \(28x\) as \(25x+3x\) in the trinomial:
\(5x^{2}+25x + 3x+15\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((5x^{2}+25x)+(3x + 15)\)
Factor out the greatest common factor from each group:
\(5x(x + 5)+3(x + 5)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((x + 5)\):
\((5x + 3)(x + 5)\)

Answer:

\((5x + 3)(x + 5)\)