Question

How do you factor the trinomial `x^2-12x+35`?

Answer 1

See a solution process below:

Explanation:

Because the `x^2` coefficient is `1` we know the coefficient for the `x` terms in the factor will also be `1`:

`(x )(x )`

Because the constant is a positive and the coefficient for the `x` term is a negative we know the sign for the constants in the factors will both be negative because a negative plus a negative is a negative and negative times a negative is a positive:

`(x - )(x - )`

Now we need to determine the factors which multiply to 35 and also add to 12:

`1 xx 35 = 35`; `1 + 35 = 36` <- this is not the factor

`5 xx 7 = 35`; `5 + 7 = 12` <- this IS the factor

`(x - 5)(x - 7)`