# Factoring & Solving Quadratic Tips

When Factoring a Trinomial, you may have noticed that there are only 2 possible signs and so only 4 possible arrangements. Having these limiting situations means that there are certain things that will always happen!

So we will let a, b, & c be any positive number.

If the sign on c is positive (sum of factors of c make b):

ax^{2} + bx + c The sign on c tells us that both sets of parentheses will have the same sign. The sign on b will tell us what that sign will be, in this case +, so (__ + __)(__ + __).

For ax^{2} – bx + c Since the sign on the b is -, they will now both be negative, so (__ – __)(__ – __).

If the sign on c is negative (difference of factors of c make b):

The sign on c tells us that the sets of parentheses will have different signs. The sign on b will tell us that the bigger factor of c will have that sign. Assuming the bigger factor is in the first set of parentheses:

ax^{2} + bx – c If the b is positive, we have (__ + __)(__ – __).

ax^{2} – bx – c If the b is negative, we have (__ – __)(__ + __).

Now when solving Quadratics we set the above factors to 0, since if the product is 0, then at least one of the factors is 0. So our signs will be the opposites for our answers!

Quadratic | Factored | Solved |

ax^{2} + bx + c |
(__ + __)(__ + __) | x = -__, -__ |

ax^{2} – bx + c |
(__ – __)(__ – __) | x = +__, +__ |

ax^{2} + bx – c |
(__ + __)(__ – __) | x = -__, +__ |

ax^{2} – bx – c |
(__ – __)(__ + __) | x = +__, -__ |