Question

Factoring trinomials

Answer 1

`c^2`
`2c^2 + 13c +21 \\4c^2 + 13(2)c + 42\\(2c + 6)(2c+7)\\(c+3)(2c+7)`

This is a way to factoring trinomials (there exist different equivalent methods).

Multiply the trinomial but the term accompanying
`c^2`. This is the second line. Then, you could take the square of the
`4c^2`, ant try to create a factor () () that will correspond to the expression in the second line. That is, we want
`4c^2 + 13(2) c + 42 = (2c + ?) (2c + ?)`

In ? we put the corresponding numbers that, if we multiply them we will obtain 42, and if we add them we will obtain 13. This numbers are 6 and 7. Then, we have
`(2c + 6) (2c +7)`

The last step is divide by the number that we multipy in the first step.