# Question Video: Dividing Polynomials Mathematics • 10th Grade

Find the quotient when 6π₯β΄ + 11π₯Β³ β 43π₯Β² β 40π₯ is divided by π₯Β² + π₯ β 8.

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### 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 weβre dividing. And it says weβre 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 weβre 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, weβre 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 weβll repeat this process again. What do we multiply to π₯ squared to make it be five π₯ cubed? Weβll 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, weβre 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 thereβs nothing left. Thereβs no remainder. So essentially, this divided evenly.

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