Factor the expression by grouping. First, the expression needs to be rewritten as $-y^{2}+ay+by+156$. To find $a$ and $b$, set up a system to be solved.
$$a+b=35$$ $$ab=-156=-156$$
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 $-156$.
Rewrite $-y^{2}+35y+156$ as $\left(-y^{2}+39y\right)+\left(-4y+156\right)$.
$$\left(-y^{2}+39y\right)+\left(-4y+156\right)$$
Factor out $-y$ in the first and $-4$ in the second group.
$$-y\left(y-39\right)-4\left(y-39\right)$$
Factor out common term $y-39$ by using distributive property.
$$\left(y-39\right)\left(-y-4\right)$$
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 $ax^{2}+bx+c=0$.
$$-y^{2}+35y+156=0$$
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.
