This week in Pre-Calculus 11, we started on some review of our next unit which is factoring and quadratics, for this week we re-learned a helpful way to solve the factors.
The hint to this entire thing is 1, 2, 3
First of all, is there one thing in common?
So, the first step is to check for any similarities between the two numbers. Because they have 5 in common, a valid equation would be 10×2 -15x. It may also be divided by x because they both have an x. To rewrite it, simply write 5x (2x-3).
Second of all, are there two terms (binomial)
So, for this one, you’ll need to pick a number that has two perfect squares. 16×2-25, for example. So all you have to do is square root both of them √16x^2 – √25 and you get (4x-5)2. Because it was a negative, you’d write it down as (4x+5) on foil (4x-5). to get 16×2-20x +20x – 25, which is the same as our initial equation 16×2-25.
Third of all,
The most important thing to remember while solving this type of problem is the product and sum. To find the total, add or subtract the integers that multiply to produce the product. The product is the sum of the equation’s first and last numbers. The middle number is the sum. Let’s pretend we have x2 +7x+10. We multiply the unseen 1 in front of the x2 and the 10 to get 10 as the product. Now we’ll take a look at the numbers that multiply to ten: 110, 25. Now we’ll see which of them you’d combine to obtain 7. It would be the 2 and 5, as 2+5=7 in this situation. There are a number of methods to get the answer from here, but using the box approach is one of the most useful.