Answer
$(2x-3)(2x-1)$
Work Step by Step
Factor the given quadratic using the $ac$-method by performing the following steps:
(1) Find the value of $ac$. The given quadratic trinomial has $a=4, b=-8, $ and $c=3$.
Thus, $ac=4(3)=12$.
(2) Look for factors $d$ and $e$ of $12$ whose sum is equal to be $(-8)$.
Note that: $12=(-6)(-2)$ and $-6+(-2) = -8$.
Thus, $d=-6$ and $e=-2$.
(3) Rewrite the quadratic trinomial as $ax^2+dx+ex+c$:
$$4x^2-8x+3=4x^2-6x-2x+3$$
(4) Factor $4x^2-6x-2x+3$ by grouping:
\begin{align*}
4x^2-6x-2x+3&=(4x^2-6x)+(-2x+3)\\
&=2x(2x-3)+(-1)(2x-3)\\
&=(2x-3)(2x-1)
\end{align*}
