solving quadratic equations by factoring steps

#Solving quadratic equations by factoring steps plus

X minus five times five X plus two, when does that equal zero? And like we saw before, well, this is just like The zeros of F of X.' Well, the zeros are, what are the X values that make F of X equal to zero? When does F of X equal zero? For what X values does F of X equal zero? That's what people are really asking when they say, 'Find the zeros of F of X.' So to do that, well, whenĭoes F of X equal zero? Well, F of X is equal to zero when this expression right over here is equal to zero, and so it sets up just like So let's say someone told you that F of X is equal to X minus five, times five X, plus two, and someone said, 'Find

$solving quadratic equations by factoring steps$

That I just wrote here, and so I'm gonna involve a function. This second expression is going to be zero, and even though this first expression isn't going to be zero in that case, anything times zero is going to be zero. And likewise, if X equals negative four, it's pretty clear that So when X equals 1/2, the first thing becomes zero, making everything, making One minus one is zero, so I don't care what you have over here. And so what's this going to be equal to? Well, two times 1/2 is one. That's going to be our first expression, and then our second expression Two times 1/2 minus one, two times 1/2 minus one. If X is equal to 1/2, what is going to happen? Well, this is going to be I think it's pretty interesting to substitute either one of these in. X could be equal to 1/2, or X could be equal to negative four. In an equation like this, you can actually have two solutions.

Two solutions here, or over here, if we wanna solve for X, we can subtract four from both sides, and we would get X isĮqual to negative four. This is interesting 'cause we're gonna have If this looks unfamiliar, I encourage you to watch videos on solving linearĮquations on Khan Academy, but you'll get X is equal Divide both sides by two, and this just straightforward solving a linear equation. If two X minus one could be equal to zero, well, let's see, you couldĪdd one to both sides, and we get two X is equal to one. X plus four is equal to zero, and so let's solve each of these. One is equal to zero, or X plus four is equal to zero. Actually, let me do the two X minus one in that yellow color. So I could write that as two X minus one needs to be equal to zero, or X plus four, or X, let me do that orange. Needs to be equal to zero, or X plus four needs to be equal to zero, or both of them needs to be equal to zero. X minus one as our A, and you could view X plus four as our B. Little bit different, but you could view two That one of those numbers is going to need to be zero. Try to multiply them so that you get zero, and you're gonna see Stuck in your brain, and I want you to think about why that is. I'm gonna put a red box around it so that it really gets Product of two quantities, and you get zero, is if one or both of So you see from this example, either, let me write this down, either A or B or both, 'cause zero times zero is zero, or both must be zero. If A is seven, the only way that you would get zero is if B is zero, or if B was five, the only way to get zero is if A is zero. Product of two numbers to equal zero without at least one of them being equal to zero? And the simple answer is no. If I had two variables, let's say A and B, and I told you A times B is equal to zero. This is expression is being multiplied by X plus four, and to get it to be equal to zero, one or both of these expressions needs to be equal to zero. Thing being multiplied is two X minus one. Things being multiplied, and it's being equal to zero. So at first, you might be tempted to multiply these things out, or there's multiple ways that you might have tried to approach it, but the key realization here is that you have two Satisfy this equation, essentially our solutions If you can figure out the X values that would We can use the zero-product property to solve quadratic equations in which we first have to factor out the greatest common factor (GCF), and for equations that have special factoring formulas as well, such as the difference of squares, both of which we will see later in this section.That we've got the equation two X minus one times X plus four is equal to zero. For example, equations such as 2+x - 6=0 is in standard form. An equation containing a second-degree polynomial is called a quadratic equation.

Solving quadratic equations by factoring steps