Factor using the ac-method.
-$$6 x ^ { 4 } + 13 x ^ { 2 } + 6$$
A) $\left( 2 x ^ { 2 } + 1 \right) \left( 3 x ^ { 2 } + 6 \right)$
B) $\left( 6 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 2 \right)$
C) $\left( 3 x ^ { 2 } - 2 \right) \left( 2 x ^ { 2 } - 3 \right)$
D) $\left( 2 x ^ { 2 } + 3 \right) \left( 3 x ^ { 2 } + 2 \right)$

Question

Quizplus · Accepted Answer

We need to find two numbers whose product is $6\cdot 6=36$ and whose sum is $13$. The numbers are $9$ and $4$. Now, we un-foil:
$$
\left(6x^2+4\right)\left(x^2+3\right).
$$ 
Both factors can be further simplified:
$$
6x^2+4=2\cdot \left(3x^2+2\right)
$$ and
$$
x^2+3=x^2+1+2=(x^2+1)+2.
$$Putting it all together, we get 
\begin{align*}
6 x ^ { 4 } + 13 x ^ { 2 } + 6  &= \left( 6 x ^ { 2 } + 4 \right) \left( x ^ { 2 } + 3 \right) \
&= \left( 2\cdot \left( 3 x ^ { 2 } + 2 \right) \right) \left( \left( x ^ { 2 } + 1 \right) + 2 \right) \
&= \boxed{(2 x ^ { 2 } + 3 ) ( 3 x ^ { 2 } + 2 ) }
\end{align*}

Factor Using the Ac-Method 6x4+13x2+66 x ^ { 4 } + 13 x ^ { 2 } + 66x4+13x2+6

Factor Using the Ac-Method $6 x ^ { 4 } + 13 x ^ { 2 } + 6$