factoring quadratic equations box method

#Factoring quadratic equations box method plus#

You just had this expression, here, and someone told you toįactor it, then you'd have to factor out the 9. You're doing the same thing toīoth sides of equations, which we've learned long ago is a The terms by 9, it won't change the equation. If you think about it, you canĭivide both sides of this equation by 9. We get 9 times x squared- actually even better, youĭon't even have to factor out of 9. Let's just figure out whatĤ05 divided by 9 is.

#Factoring quadratic equations box method plus#

Now, is there any commonįactor to these numbers right here? Well 405, 4 plus 0 plus 5 is 9,

Right-hand side equals 0, and your left-hand side is 9x Now we want our quadraticĮxpression to be equal to 0. This is the same thingĪs 9x times x plus 4 is equal to 405. So what do we get here? If we distribute this x Volume of the box is 405 cubic units, is equal to 405. Would be x plus 4 times the length - times x- times 9. Volume, what would it be? Well it would be the width- it In units, what are theĭimensions of the box? Well, they also tell us that Is x plus 4 units, and the height is 9 units. It as units, keep it as general as possible.

But as you can see, and as andrew pointed out, even though the point is moving -4, the distance from where it was to where it is is |-4| = 4.Ĥ05 cube units, or I guess cubic units. Having said that, a time you might see something that looks like a negative distance is just a way of saying, 'to the left.' If I had a list of distances that a point had traveled over the number line, such as, I would read that as: the point first moved 2 to the right, then 5 to the right, then 4 to the left, and finally 2 to the left. So negative distance is like dividing by zero, if you try, you just get silly results. If it could be negative, then the system we have wouldn't work - you would have conundrums and paradoxes such as arriving before you leave. The first rule of metric spaces is d(a,b)≥0, that is, distance is non negative. Now, there are a lot of different types of distances, and the math ones, at this level, have one thing in common, they are built on the notion of the 'metric space' (all the mathematics you will be doing here at Khan is based on metric space, though talking about it is a more advanced subject). If you want to go from A to B, and distance equals velocity times time, d=vt and d was negative, that would mean you would get to B before you even left A!