Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.
$$-x^{2}+2x+48$$
Factor the expression by grouping. First, the expression needs to be rewritten as $-x^{2}+ax+bx+48$. To find $a$ and $b$, set up a system to be solved.
$$a+b=2$$ $$ab=-48=-48$$
Since $ab$ is negative, $a$ and $b$ have the opposite signs. Since $a+b$ is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product $-48$.
Rewrite $-x^{2}+2x+48$ as $\left(-x^{2}+8x\right)+\left(-6x+48\right)$.
$$\left(-x^{2}+8x\right)+\left(-6x+48\right)$$
Factor out $-x$ in the first and $-6$ in the second group.
$$-x\left(x-8\right)-6\left(x-8\right)$$
Factor out common term $x-8$ by using distributive property.
$$\left(x-8\right)\left(-x-6\right)$$
Steps Using the Quadratic Formula
Quadratic polynomial can be factored using the transformation $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$, where $x_{1}$ and $x_{2}$ are the solutions of the quadratic equation $ax^{2}+bx+c=0$.
$$-x^{2}+2x+48=0$$
All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. The quadratic formula gives two solutions, one when $±$ is addition and one when it is subtraction.
