Question

factor.
$2z^2 + 13z + 20$

Explanation:

Step1: Identify \(a\), \(b\), \(c\)

For \(2z^2 + 13z + 20\), \(a = 2\), \(b = 13\), \(c = 20\).

Step2: Find two numbers

Find two numbers that multiply to \(a\times c=2\times20 = 40\) and add to \(b = 13\). The numbers are \(5\) and \(8\) (since \(5\times8 = 40\) and \(5 + 8 = 13\)).

Step3: Split the middle term

Rewrite the middle term using these numbers: \(2z^2+5z + 8z + 20\).

Step4: Group and factor

Group the first two and last two terms: \((2z^2 + 5z)+(8z + 20)\). Factor out the GCF from each group: \(z(2z + 5)+4(2z + 5)\). Now factor out the common binomial factor \((2z + 5)\): \((2z + 5)(z + 4)\).

Answer:

\((2z + 5)(z + 4)\)