Hi Bailey,

I can help get you started. Look at the first factor

\[6a^2 - 5a + 1.\]

$6$ can be factored as $6 \times 1$ or $3 \times 2$ and hence, if $6a^2 - 5a + 1$ can be factored it is

\[6a^2 - 5a + 1 = (6a \pm \mbox{?})(a \pm \mbox{?})\]

or

\[6a^2 - 5a + 1 = (3a \pm \mbox{?})(2a \pm \mbox{?}).\]

$1$ factors as $1 \times 1$ and hence the question marks are all $1.$ Since the constant term is positive and the middle term $(-5a)$ is negative the signs must be negative and hence if $6a^2 - 5a + 1$ can be factored it is

\[6a^2 - 5a + 1 = (6a - 1)(a -1)\]

or

\[6a^2 - 5a + 1 = (3a -1)(2a -1).\]

Which one gives a middle term of $-5a?$

Now you factor $(8a^2-6a+1)$ and $(12a^2-7a+1).$

Penny