Quickly master how to solving quadratic equations by factoring. Watch more lessons like this and try our practice at https://www.studypug.com/algebra-help/quadratic-equations/solve-quadratic-equations-by-factoring
Review the chapter on “Factoring” to refresh your memory if you don’t quite remember how to factor polynomials. It will definitely help you solve the questions in this lesson!
Solve the equation by factoring. Now, for those of you that forget how to do factoring, now is a good time to go back to an earlier chapter called “factoring,” where I taught all the techniques and tricks to do factoring. Cool. Back to this question here. So, to factor this trinomial, the first thing you got to ask yourself is, “well, between the numbers here, is there a common factor?” Well all three numbers are even numbers, so that means they must be divisible by 2, so let’s factor out 2. Okay? And what do we have left inside the bracket? Well for the first term, 2x squared, factor out the 2, what do we have left? Just x squared right? Now, for the second term, negative 12x. Now what do we factor out? We factor out 2, so you got to divide this by 2. So what do we have left? Negative 12 divided by 2, we have negative 6x So we have negative 6x left inside the bracket. Now for the third term, the constant term, positive 10, what do we factor out again? We factored out 2, so divide by 2, so we have 5 left inside the bracket. Positive 5. Okay? Cool. Now, how do we factor this trinomial inside the bracket? Well, do you remember a very powerful technique called cross multiply, then check? Right? So let’s use that technique to factor this trinomial, okay? So, look at the leading term x squared, we can break it apart as x times x right? Now, look at the constant term, positive 5. Well, positive 5 can be positive times positive 1. Right? Because positive 5 times positive 1 is positive 5. But is zero another option? Yes. Negative 5 times negative 1 is also positive 5. Because negative times negative, we get positive. And see, the negative is the better choice here because check this out, the middle term we are looking for is negative. Right? So, negative should be the better choice here. Okay? So now let’s do cross-multiply, then check. So, cross-multiply this way, negative 5 times x, we get negative 5. Cross-multiply this way, x times negative 1, we get negative x. And combine everything here what do we have? After cross-multiply we got to what? Check, right? So that’s why the technique is called cross-multiply, then check. Okay? So, now we have to check here, so combine everything on the bottom line here, we have negative 6x. Now you got to ask yourself, “Does this match the middle term?” Yes, negative 6x. That means we are good. See? That means our factoring is correct. So now, two factors. First factor is x minus 5. Second factor is right here, x minus 1. Now the rest is easy. To solve this equation, wow super easy. Ask yourself, guys. . . look at the first bracket here. What x value will make this whole thing equal to zero? Well, would you say x must be 5 because 5 minus 5 is zero. Right? Now what x value will make this whole thing equal to zero? X must be what? One right? Because 1 minus 1 is zero. And guess what? That’s the answer. Right? So the solution for this quadratic equation is x equals 5 and x equals 1. So we have two solutions for x.
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