Question

factor: 2z² + 21z + 10

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times10 = 20\) and add up to \(21\). The numbers are \(20\) and \(1\) since \(20\times1 = 20\) and \(20 + 1=21\).

Step2: Split the middle term

Rewrite the middle term \(21z\) as \(20z+z\):
\(2z^{2}+20z + z+ 10\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((2z^{2}+20z)+(z + 10)\)
Factor out the greatest common factor from each group:
\(2z(z + 10)+1(z + 10)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((z + 10)\):
\((2z + 1)(z + 10)\)

Answer:

\((2z + 1)(z + 10)\)