Question

factor the trinomial: $5x^2 + 8x + 3$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times3 = 15\) and add up to \(8\). The numbers are \(5\) and \(3\) since \(5\times3 = 15\) and \(5 + 3=8\).

Step2: Rewrite the middle term

Rewrite \(8x\) as \(5x+3x\) in the trinomial:
\(5x^{2}+5x + 3x+3\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((5x^{2}+5x)+(3x + 3)\)
Factor out the greatest common factor from each group:
\(5x(x + 1)+3(x + 1)\)

Step4: Factor out the common binomial

Factor out \((x + 1)\):
\((5x+3)(x + 1)\)

Answer:

\((5x + 3)(x + 1)\)