Question

How do you factor the expression `6x^2 + 5x +1`?

Answer 1

See a solution process below:

Explanation:

Because the constant is `1` we know the constant for the factored terms will also be `1`:

`( 1)( 1)`

Because the constant is a positive and the coefficient for the `x` term is also positive we know the signs for the constants in the factors will both be positive:

`( + 1)( + 1)`

Now we need to determine the factors which multiply to 6 and also add to 5 for the coefficients of the `x` terms in the factors:

`1 xx 6 = 6`; `1 + 6 = 7` <- this is not the factor

`2 xx 3 = 6`; `2 + 3 = 5` <- this IS the factor

`(2x + 1)(3x + 1)`