Consider $1-3x-18x^{2}$. Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.
$$-18x^{2}-3x+1$$
Factor the expression by grouping. First, the expression needs to be rewritten as $-18x^{2}+ax+bx+1$. To find $a$ and $b$, set up a system to be solved.
$$a+b=-3$$ $$ab=-18=-18$$
Since $ab$ is negative, $a$ and $b$ have the opposite signs. Since $a+b$ is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product $-18$.
$$1,-18$$ $$2,-9$$ $$3,-6$$
Calculate the sum for each pair.
$$1-18=-17$$ $$2-9=-7$$ $$3-6=-3$$
The solution is the pair that gives sum $-3$.
$$a=3$$ $$b=-6$$
Rewrite $-18x^{2}-3x+1$ as $\left(-18x^{2}+3x\right)+\left(-6x+1\right)$.
$$\left(-18x^{2}+3x\right)+\left(-6x+1\right)$$
Factor out $3x$ in $-18x^{2}+3x$.
$$3x\left(-6x+1\right)-6x+1$$
Factor out common term $-6x+1$ by using distributive property.
