Question

How do you factor `14x ^ { 2} - 77x + 217`?

Answer 1

`7  (2x^2 - 11 + 31)`

Explanation:

Each term is a multiple of `7`, so you can factor out `7` from each term and write it outside a parentheses grouping symbol, like this:

Factor this expression:
`14x^2−77x+217`

Factor out `7` from each term
`7 (2x^2 - 11 + 31)`
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

You can check if this was done correctly by distributing the `7` back in to each of the terms in the parentheses.

If it was factored correctly, distributing the `7` should bring back the original expression.

Distribute the `7`
`7 (2x^2 - 11 + 31)`

After you clear the parentheses by distributing, you get this:
`14x^2 - 77 + 217`
This is the original expression back again, so the factoring was done correctly.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~

This is the final answer because the trinomial cannot be factored any further.

Answer
`7 (2x^2 - 11 + 31)`