This lesson addresses some more difficult factoring problems. If you would like to see some easier problems before you try these, check out the Level 1 Factoring lesson.
Factoring Quadratics Review
In the Level 1 lesson, all of the quadratics we factored started with an x-squared term. Let's look at one quick problem to review before we try some harder ones.
In order to factor this, we need to identify the two binomials that multiply to this quadratic. In other words, we need to know ( ? ) times ( ? ) will equal this quadratic expression. We know that the x-squared term will come from multiplying the "Firsts" if you use FOIL - this means that there must be an x in both Firsts spots. This gives us:
Now let's look at the constant at the end. There's a positive 8 at the end. This means the numbers in the "Lasts" spots must multiply to 8. A common assumption students make is to think that since the two numbers multiply to a positive 8, that they must both be positive. However, two negatives also multiply to a positive, so that tells us that we either have two plus signs or two negative signs. It can't be one of each because then they would multiply to a -8 at the end. So now we have it narrowed down to this:
So which one is it? To tell, always look at the term in the middle. Our term in the middle is -9x. The only way for the middle term to end up negative will be to use the option with two negative signs. This means it must be this:
Next we need to look at the options for the "Lasts" spots. We know they must multiply to 8, so let's list out the options.
Options for Lasts spots:
1 and 8
2 and 4
Now we can just pick a combination and try it to see if it works. Distribute (use FOIL) to see if it comes out to the quadratic we've been given. If it doesn't work, try a different option. Let's try the 1 and 8 first.
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