Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.
$$-15x^{2}+17x+4$$
Factor the expression by grouping. First, the expression needs to be rewritten as $-15x^{2}+ax+bx+4$. To find $a$ and $b$, set up a system to be solved.
$$a+b=17$$ $$ab=-15\times 4=-60$$
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 $-60$.
Rewrite $-15x^{2}+17x+4$ as $\left(-15x^{2}+20x\right)+\left(-3x+4\right)$.
$$\left(-15x^{2}+20x\right)+\left(-3x+4\right)$$
Factor out $-5x$ in the first and $-1$ in the second group.
$$-5x\left(3x-4\right)-\left(3x-4\right)$$
Factor out common term $3x-4$ by using distributive property.
$$\left(3x-4\right)\left(-5x-1\right)$$
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 $ax^{2}+bx+c=0$.
$$-15x^{2}+17x+4=0$$
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.
Now solve the equation $x=\frac{-17±23}{-30}$ when $±$ is plus. Add $-17$ to $23$.
$$x=\frac{6}{-30}$$
Reduce the fraction $\frac{6}{-30}$ to lowest terms by extracting and canceling out $6$.
$$x=-\frac{1}{5}$$
Now solve the equation $x=\frac{-17±23}{-30}$ when $±$ is minus. Subtract $23$ from $-17$.
$$x=-\frac{40}{-30}$$
Reduce the fraction $\frac{-40}{-30}$ to lowest terms by extracting and canceling out $10$.
$$x=\frac{4}{3}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $-\frac{1}{5}$ for $x_{1}$ and $\frac{4}{3}$ for $x_{2}$.
Multiply $\frac{-5x-1}{-5}$ times $\frac{-3x+4}{-3}$ by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.
