Accompanying Resource: Printable Study Guide Factoring QuadraticsThere are a few different ways you can factor a quadratic expression (check out a lesson on factoring if this isn't familiar to you). You can use educated guessandcheck and use FOIL to see if you've factored it correctly. Let's say we have to factor the quadratic below:
We could use educated guessandcheck to factor this quadratic. We know that the numbers in the LAST spots must multiply to 8. This means we could try 1 and 8 or 2 and 4. In order to end up with a 6x in the middle, we need to use the 2 and the 4. You could also use the Quadratic Formula to find the roots of the quadratic. We need to plug in 1 for a, 6 for b and 8 for c. We can see that it simplifies to 2 and 4. Remember, the Quadratic Formula gives you the roots (zeros). These are the values that make the expression equal to 0. We can use the roots to write the factors. If 2 is a root, that means (x +2) is a factor. If you plug 2 into (x + 2), it equals 0. Likewise, if 4 is a root, that means (x + 4) is a factor. 

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