Apply the distributive property by multiplying each term of $x+5$ by each term of $x+3$.
$$factor(x^{2}+3x+5x+15+5x\times 2)$$
Combine $3x$ and $5x$ to get $8x$.
$$factor(x^{2}+8x+15+5x\times 2)$$
Multiply $5$ and $2$ to get $10$.
$$factor(x^{2}+8x+15+10x)$$
Combine $8x$ and $10x$ to get $18x$.
$$factor(x^{2}+18x+15)$$
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 $ax^{2}+bx+c=0$.
$$x^{2}+18x+15=0$$
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.
$$x=\frac{-18±\sqrt{18^{2}-4\times 15}}{2}$$
Square $18$.
$$x=\frac{-18±\sqrt{324-4\times 15}}{2}$$
Multiply $-4$ times $15$.
$$x=\frac{-18±\sqrt{324-60}}{2}$$
Add $324$ to $-60$.
$$x=\frac{-18±\sqrt{264}}{2}$$
Take the square root of $264$.
$$x=\frac{-18±2\sqrt{66}}{2}$$
Now solve the equation $x=\frac{-18±2\sqrt{66}}{2}$ when $±$ is plus. Add $-18$ to $2\sqrt{66}$.
$$x=\frac{2\sqrt{66}-18}{2}$$
Divide $-18+2\sqrt{66}$ by $2$.
$$x=\sqrt{66}-9$$
Now solve the equation $x=\frac{-18±2\sqrt{66}}{2}$ when $±$ is minus. Subtract $2\sqrt{66}$ from $-18$.
$$x=\frac{-2\sqrt{66}-18}{2}$$
Divide $-18-2\sqrt{66}$ by $2$.
$$x=-\sqrt{66}-9$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $-9+\sqrt{66}$ for $x_{1}$ and $-9-\sqrt{66}$ for $x_{2}$.
