Factor Trinomials of the Form $a{x}^2+bx+c$Using Trial and Error.

$-16x^2-32x-16$

Consider the trinomial.

$-16x^2-32x-16$

The trinomial $-16x^2-32x-16$is given in descending order.

There is a greatest common factor in the given trinomial.

Factor the greatest common factor.

localid="1645097212530" $-16x^2-32x-16=-16(x^2+2x+1)$

The first term of the trinomial $x^2+2x+1$is localid="1645096237773" $x^2$.

So, the only factors of $x^2$are as follows:

$x^2=x·x$

The last term of the trinomial $x^2+2x+1$is $1$.

Since all the terms in the polynomial$x^2+2x+1$ is positive, all the factors of the last term will be positive.

The only factors of localid="1645098817372" $1$are as follows:

$1=1·1$

From the table, conclude that the only combination is $(x+1)(x+1)$.

So, the factor of the given trinomial is $-16(x+1)(x+1)$.

$\begin{array}{rcl}-16(x+1)(x+1)& =& -16(x^2+x+x+1)\\ & =& -16(x^2+2x+1)\\ & =& -16x^2-32x-16\end{array}$

Hence, the factor is $-16(x+1)(x+1)$.