Section 6.3: Factoring Trinomials of the Form $ax^2+bx+c$ Worksheet 6.3
Recall: One way factor, say, $x^2+3x+2$, is to write
$$x^2+3x+2=(x+\,\,\,\,)(x+\,\,\,\,)$$
and fill in the numbers by trial and error.
We can do something similar for trinomials of the form $ax^2+bx+c$.
Example: $15r^2-28r+12$
Other Examples: Factor the following expressions.
$10t^2â19tâ12$
$-24q^2+38q-15$
$24\phi^2-38\phi x+15x^2$
A More Systematic Method: The $ac$ Method
To factor $ax^2+bx+c$, find two numbers whose
sum is $b$ and whose product is $ac$.
Example: Factor $8z^2+37z-15$
A good first step is to make a table of factors.
$$
\begin{array}{c|c}
ac=8(-15)=-120 & \mbox{sum}\\ \hline
& \\
& \\
& \\
& \\
\end{array}
$$
More Examples
$15x^2+2x-8$
$12x^2+8x u-15u^2$
$3q^2-25q+12$