Consider $-4x^{2}-1-5x$. Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.
$$-4x^{2}-5x-1$$
Factor the expression by grouping. First, the expression needs to be rewritten as $-4x^{2}+ax+bx-1$. To find $a$ and $b$, set up a system to be solved.
$$a+b=-5$$ $$ab=-4\left(-1\right)=4$$
Since $ab$ is positive, $a$ and $b$ have the same sign. Since $a+b$ is negative, $a$ and $b$ are both negative. List all such integer pairs that give product $4$.
$$-1,-4$$ $$-2,-2$$
Calculate the sum for each pair.
$$-1-4=-5$$ $$-2-2=-4$$
The solution is the pair that gives sum $-5$.
$$a=-1$$ $$b=-4$$
Rewrite $-4x^{2}-5x-1$ as $\left(-4x^{2}-x\right)+\left(-4x-1\right)$.
$$\left(-4x^{2}-x\right)+\left(-4x-1\right)$$
Factor out $-x$ in the first and $-1$ in the second group.
$$-x\left(4x+1\right)-\left(4x+1\right)$$
Factor out common term $4x+1$ by using distributive property.
