Solve $\color{blue}{x^2-8x+15 = 0}$ using factoring.

$$ \color{blue}{ x_1 = 3 }~~ \text{and}~~ \color{blue}{ x_2 = 5 } $$

First we need to factor trinomial $ \color{blue}{ x^2-8x+15 } $ and than we use factored form to solve an equation $ \color{blue}{ x^2-8x+15 = 0} $.

** Step 1:** Identify constants $ \color{blue}{ b }$ and $\color{red}{ c }$.
( $ \color{blue}{ b }$ is a number in front of the $ x $ term and $ \color{red}{ c } $ is a constant). In our case:

Now we must discover two numbers that sum up to $ \color{blue}{ -8 } $ and multiply to $ \color{red}{ 15 } $.

** Step 2:** Find out pairs of numbers with a product of $\color{red}{ c = 15 }$.

PRODUCT = 15 | |

1 15 | -1 -15 |

3 5 | -3 -5 |

** Step 3:** Find out which pair sums up to $\color{blue}{ b = -8 }$

PRODUCT = 15 and SUM = -8 | |

1 15 | -1 -15 |

3 5 | -3 -5 |

** Step 4:** Put -3 and -5 into placeholders to get factored form.

** Step 5:** Set each factor to zero and solve equations.

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