Consider $-2x^{2}+15-7x$. Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.
$$-2x^{2}-7x+15$$
Factor the expression by grouping. First, the expression needs to be rewritten as $-2x^{2}+ax+bx+15$. To find $a$ and $b$, set up a system to be solved.
$$a+b=-7$$ $$ab=-2\times 15=-30$$
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 $-30$.
$$1,-30$$ $$2,-15$$ $$3,-10$$ $$5,-6$$
Calculate the sum for each pair.
$$1-30=-29$$ $$2-15=-13$$ $$3-10=-7$$ $$5-6=-1$$
The solution is the pair that gives sum $-7$.
$$a=3$$ $$b=-10$$
Rewrite $-2x^{2}-7x+15$ as $\left(-2x^{2}+3x\right)+\left(-10x+15\right)$.
$$\left(-2x^{2}+3x\right)+\left(-10x+15\right)$$
Factor out $-x$ in the first and $-5$ in the second group.
$$-x\left(2x-3\right)-5\left(2x-3\right)$$
Factor out common term $2x-3$ by using distributive property.
