Step 1

We have to factorize the following expressions:

\(6y^{2}-5y=\)?

\(9a^{3}-3a^{2}=\)?

\(x^{2}+xy+3xz=\)?

Factorization is the process of taking common term from the terms of the expression.

Factorizing first part:

\(6y^{2}-5y=y(6y-5)\)

Hence, factorization of the expression is \(y(6y−5).\)

Step 2

Factorizing second part:

\(9a^{3}-3a^{2}=3a^{2}\times 3a-3a^{2}\)

\(=3a^{2}(3a-1)\)

Hence, factorization of the expression is \(3a^{2}(3a-1)\).

Factorizing third part:

\(x^{2}+xy+3xz=x(x+y+3z)\)

Hence, factorization of the expression is \(x(x+y+3z).\)