### Video Transcript

Find the quotient when six π₯ to
the fourth plus 11π₯ cubed minus 43π₯ squared minus 40π₯ is divided by π₯ squared
plus π₯ minus eight.

So we are finding a quotient, which
means that weβre dividing. And it says weβre taking six π₯ to
the fourth plus 11π₯ cubed minus 43π₯ squared minus 40π₯ and dividing it by π₯
squared plus π₯ minus eight. So to do this, we look at the first
terms. And we think, how many π₯ squareds
go into six π₯ to the fourth? Or what do we multiply π₯ squared
by to make it be six π₯ to the fourth?

We would need to multiply π₯
squared by six π₯ squared. That would give us six π₯ to the
fourth. And we put the π₯ squared term
above the π₯ squared term here. This keeps us organised. Now, we need to begin multiplying
six π₯ squared to π₯ squared plus π₯ minus eight. So six π₯ squared times π₯ squared
is six π₯ to the fourth power.

Now, we take six π₯ squared times
π₯, which is six π₯ cubed. And notice weβre putting the π₯ to
the fourth powers and π₯ cubes underneath each other. And now we take six π₯ squared
times negative eight, giving us negative 48π₯ squared. And we will be subtracting. These cancel. And then, 11π₯ cubed minus six π₯
cubed will be five π₯ cubed.

Now, we have negative 43π₯ squared
minus negative 48π₯ squared. So really, weβre taking negative
43π₯ squared plus 48π₯ squared, which is positive five π₯ squared. And we will need to bring down the
minus 40π₯.

So now weβll repeat this process
again. What do we multiply to π₯ squared
to make it be five π₯ cubed? Weβll need to multiply π₯ squared
by five π₯. And now we distribute. So five π₯ times π₯ squared is five
π₯ cubed. Five π₯ times π₯ is five π₯
squared. And five π₯ times negative eight is
negative 40π₯. And remember, weβre
subtracting.

So five π₯ cubed minus five π₯
cubed cancels. Five π₯ squared minus five π₯
squared cancels. And then negative 40π₯ minus
negative 40π₯ is negative 40π₯ plus 40π₯. So those cancel as well, which
means thereβs nothing left. Thereβs no remainder. So essentially, this divided
evenly.

And our quotient, our answer will
be six π₯ squared plus five π₯.