Question

Find the factored form of this trinomial.
a^2-10a-24

Answer 1

This will factor into two binomials.
\[\large a^2-10a-24\]
We want `factors` of -24 that will `add` to -10.

Here are a couple factors we can try,
\[\large -6 \times 4 =-24\]But when we try to add these numbers,\[\large -6+4\neq -10\]
They didn't `add` up to -10.
Hmm those didn't work out for us.
We need to try some other factors.

Answer 2

How about these maybe.\[\large -12 \times 2\]or\[\large 12 \times (-2)\]

Maybe one of these sets of factors will work :D Hmmm

Answer 3

\[\large -12 \times 2 = -24\]Adding them we get,\[\large \color{orangered}{-12}+\color{royalblue}{2}=-10\]Yay it worked! So we have determined that these factors will be included in our binomials.

\[\large a^2-10a-24 \qquad = \qquad (a\color{orangered}{-12})(a+\color{royalblue}{2})\]

Answer 4

ty