Question

Factor the following by taking on the greatest common factor 14a^3 + 35a^2 +42a

Answer 1

Let's break apart each term into its factors:

`\begin{gathered} 14a^3=2\cdot7\cdot a\cdot a\cdot a \\ 35a^2=5\cdot7\cdot a\cdot a \\ 42a=2\cdot3\cdot7\cdot a \end{gathered}`

The common factors are

7 * a

That is,

`7\cdot a=7a`

Now, factorizing the expression, we have:

`\begin{gathered} 14a^3+35a^2+42a \\ =7a(2a^2+5a+6) \end{gathered}`Answer
`7a(2a^2+5a+6)`