Question

How do you factor `x^2 - 8x + 15`?

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 15 and also add to 8:

`1 xx 15 = 15`; `1 + 15 = 16` <- this is not the factor

`3 xx 5 = 15`; `3 + 5 = 8` <- this IS the factor

`(x - 3)(x - 5)`