Question

factor the trinomial:
$5x^2 + 29x + 20$
answer attempt 1 out of 2

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times20 = 100\) and add up to \(29\). The numbers are \(25\) and \(4\) since \(25\times4 = 100\) and \(25 + 4=29\).

Step2: Split the middle term

Rewrite the middle term \(29x\) as \(25x+4x\):
\(5x^{2}+25x + 4x+20\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((5x^{2}+25x)+(4x + 20)\)
Factor out the greatest common factor from each group:
\(5x(x + 5)+4(x + 5)\)

Step4: Factor out the common binomial

Factor out \((x + 5)\):
\((5x + 4)(x + 5)\)

Answer:

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