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{{ printedBook.courseTrack.name }} {{ printedBook.name }} To factor a trinomial with a leading coefficient of one, think of the process as multiplying two binomials in reverse. Let's start by taking a look at the constant term.
$x_{2}−4x−21⇔x_{2}+(-4)x+(-21) $
In this case, the constant term is $-21.$ This is a *negative* number, so for the product of the constant terms in the factors to be *negative*, these constants must have opposite signs (one positive and one negative.)

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

$1$ and $-21$ | $-21$ |

$-1$ and $21$ | $-21$ |

$3$ and $-7$ | $-21$ |

$-3$ and $7$ | $-21$ |

Next, let's consider the coefficient of the linear term. $x_{2}+(-4)x+(-21) $ We need the sum of the factors that produced the constant term to equal the coefficient of the linear term, $-4.$

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

$1$ and $-21$ | $-20$ |

$-1$ and $21$ | $20$ |

$3$ and $-7$ | $-4$ |

$-3$ and $7$ | $4$ |

We found the numbers whose product is $-21$ and whose sum is $-4.$ These numbers are $3$ and $-7.$ We can now rewrite the given expression as a product of two factors. $x_{2}−4x−21⇔(x+3)(x−7) $