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# Factor trinomial $$ \color{blue}{ 6x^2-7x+18 } $$

## Answer

This quadratic trinomial cannot be factored.

## Explanation

** Step 1:** **Identify constants $ a $ , $ b $ and $ c $.**

$ a $ is a number in front of the $ x^2 $ term $ b $ is a number in front of the $ x $ term and $ c $ is a constant. In this case:

$$ a = 6 , b = -7 ~ \text{ and } ~ c = 18 $$

** Step 2:** Multiply the leading coefficient $\color{blue}{ a = 6 }$ by
the constant term $\color{blue}{c = 18} $.

$$ a \cdot c = 108 $$

** Step 3:** Find out two numbers that multiply to $ a \cdot c = 108 $ and add to $ b = -7 $.

** Step 4:** All pairs of numbers with a product of $ 108 $ are:

PRODUCT = 108 |

1 108 | -1 -108 |

2 54 | -2 -54 |

3 36 | -3 -36 |

4 27 | -4 -27 |

6 18 | -6 -18 |

9 12 | -9 -12 |

** Step 5:** Find out which factor pair sums up to $\color{blue}{ b = -7 }$

** Step 6:** Because none of these pairs will give us a sum of $ \color{blue}{ -7 }$, we conclude the polynomial cannot be factored.