Accompanying Resource: Printable Study Guide
There 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 guess-and-check 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 guess-and-check 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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