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{{ printedBook.courseTrack.name }} {{ printedBook.name }} To factor a trinomial with a leading coefficient of $1,$ we need to find two numbers whose product is the independent term.
$x_{2}−10x+24 $
In this case, we have that the constant term is $24.$ This is a *positive* number, so for a product to be *positive*, the factors must have the same sign (both positive or both negative).

Factor Constants | Product of Constants |
---|---|

$1$ and $24$ | $24$ |

$-1$ and $-24$ | $24$ |

$2$ and $12$ | $24$ |

$-2$ and $-12$ | $24$ |

$3$ and $8$ | $24$ |

$-3$ and $-8$ | $24$ |

$4$ and $6$ | $24$ |

$-4$ and $-6$ | $24$ |

Next, let's consider the coefficient of the linear term. $x_{2}−10x+24 $ In this case, since the linear coefficient is $-10,$ we need the sum of the factors to be $-10.$

Factors | Sum of Factors |
---|---|

$1$ and $24$ | $25$ |

$-1$ and $-24$ | $-25$ |

$2$ and $12$ | $14$ |

$-2$ and $-12$ | $-14$ |

$3$ and $8$ | $11$ |

$-3$ and $-8$ | $-11$ |

$4$ and $6$ | $10$ |

$-4$ and $-6$ | $-10$ |